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Ho, Son Hong.
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Numerical modeling and simulation for analysis of convective heat and mass transfer in cryogenic liquid storage and HVAC&R applications
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by Son Hong Ho.
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[Tampa, Fla.] :
b University of South Florida,
2007.
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ABSTRACT: This work presents the use of numerical modeling and simulation for the analysis of transport phenomena in engineering systems including zero boiloff (ZBO) cryogenic storage tanks for liquid hydrogen, refrigerated warehouses, and humanoccupied airconditioned spaces. Seven problems of medium large spaces in these fields are presented. Numerical models were developed and used for the simulation of fluid flow and heat and mass transfer for these problems. Governing equations representing the conservation of mass, momentum, and energy were solved numerically resulting in the solution of velocity, pressure, temperature, and species concentration(s). Numerical solutions were presented as 2D and 3D plots that provide more insightful understanding of the relevant transport phenomena. Parametric studies on geometric dimensions and/or boundary conditions were carried out.Four designs of ZBO cryogenic liquid hydrogen storage tank were studied for their thermal performance under heat leak from the surroundings. Steady state analyses show that higher flow rate of forced fluid flow yields lower maximum fluid temperature. 3D simulation provides the visualization of the complex structures of the 3D distributions of the fluid velocity and temperature. Transient analysis results in the patterns of fluid velocity and temperature for various stages of a proposed cooling cycle and the prediction of its effective operating term. A typical refrigerated warehouse with a set of ceiling type cooling units were modeled and simulated with both 2D and 3D models. It was found that if the cooling units are closer to the stacks of stored packages, lower and more uniform temperature distribution can be achieved.The enhancement of thermal comfort in an airconditioned residential room by using a ceiling fan was studied and quantified to show that thermal comfort at higher temperature can be improved with the use of ceiling fan. A 3D model was used for an analysis of thermal comfort and contaminant removal in a hospital operating room. It was found that if the wall supply grilles are closer to the center, the system has better performance in both contaminant removal and thermal comfort. A practical guideline for using CFD modeling in indoor spaces with an effective meshing approach is also proposed.
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Dissertation (Ph.D.)University of South Florida, 2007.
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Includes bibliographical references.
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Text (Electronic dissertation) in PDF format.
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System requirements: World Wide Web browser and PDF reader.
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Title from PDF of title page.
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Advisor: Muhammad M. Rahman, Ph.D.
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Computational fluid dynamics.
Liquid hydrogen.
Zero boiloff.
Refrigerated storage.
Thermal comfort.
Contaminant removal.
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Dissertations, Academic
z USF
x Mechanical Engineering
Doctoral.
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t USF Electronic Theses and Dissertations.
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u http://digital.lib.usf.edu/?e14.2266
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Numerical Modeling and Simula tion for Analysis of Convective Heat and Mass Transfer in Cryogenic Liquid Storage and HVAC&R Applications by Son Hong Ho A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Muhammad M. Rahman, Ph.D. Luis Rosario, Ph.D. Frank Pyrtle, III, Ph.D. Mahmood H. Nachabe, Ph.D. Amy L. Stuart, Ph.D. Date of Approval: July 19, 2007 Keywords: computational fluid dynamics, li quid hydrogen, zero boiloff, refrigerated storage, thermal comfort, contaminant removal Copyright 2007, Son Hong Ho
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Note to Reader The original of this document contains colo r that is necessary fo r understanding the data. The original dissertation is on file with the USF library in Tampa, Florida.
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Dedication To my parents, for their unbounded love and support.
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Acknowledgments The author would like to thank his majo r professor, Dr. Muhammad Mustafizur Rahman, for his guidance and encouragement. The financial support for the research on cryogenic storage for liquid hydrogen was rece ived from the National Aeronautics and Space Administration (NASA) unde r contract number NAG32751.
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i Table of Contents List of Tables v List of Figures vi List of Symbols x Abstract xv Chapter 1 Introduction 1 1.1 Cryogenic Liquid Hydrogen Storage 1 1.2 Refrigerated Warehousing 6 1.3 Indoor Environment Control 11 Chapter 2 Computational Modeling and Simulation 20 2.1 Governing Equations 20 2.1.1 Conservation of Mass 20 2.1.2 Conservation of Momentum 21 2.1.3 Conservation of Energy 22 2.1.4 Mixing Length Turbulence Model 22 2.2 Boundary Conditions 23 2.3 Relevant Formulas for Indoor Environment 24 2.3.1 Relative Humidity 24 2.3.2 PMVPPD Model 25 2.4 Numerical Solution Procedure 26 2.4.1 Preprocessing and Solution Algorithms 26 2.4.2 Postprocessing 29 2.5 Problems Under Study 30 Chapter 3 Analysis of Heat Transfer in Cryogenic Liquid Hydrogen Tank with Arrays of Injection Nozzles 32 3.1 Problem Description 32 3.2 Computational Model 36 3.2.1 Governing Equations 36 3.2.2 Boundary Conditions 36 3.2.3 Numerical Solution 37 3.2.4 Dimensionless Parameters 39 3.3 Results and Discussion 40 3.4 Conclusions 52
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iiChapter 4 Analysis of Heat Transfer in Cryogenic Liquid Hydrogen Tank with Heat Pipe and Array of PumpNozzle Units 54 4.1 Problem Description 54 4.2 Computational Model 57 4.2.1 Governing Equations 57 4.2.2 Boundary Conditions 57 4.2.3 Numerical Solution 58 4.2.4 Dimensionless Parameters 60 4.3 Results and Discussion 62 4.4 Conclusions 75 Chapter 5 ThreeDimensional Analysis of Heat Transfer in Cryogenic Liquid Hydrogen Tank with Heat Pipe and Lateral PumpNozzle Unit 76 5.1 Problem Description 76 5.2 Computational Model 78 5.2.1 Governing Equations 78 5.2.2 Boundary Conditions 79 5.2.3 Numerical Solution 80 5.3 Results and Discussion 82 5.4 Conclusions 92 Chapter 6 Transient Analysis of Heat Transfer in Cryogenic Liquid Hydrogen Tank with Heat Pipe and Axial PumpNozzle Unit 94 6.1 Problem Description 94 6.2 Computational Model 95 6.2.1 Governing Equations 95 6.2.2 Boundary Conditions 97 6.2.3 Numerical Solution 97 6.3 Results and Discussion 99 6.4 Conclusions 104 Chapter 7 Analysis of Cooling Perfor mance in Refrigerated Warehouse with Ceiling Type Refrigeration Units 108 7.1 Problem Description 108 7.2 Computational Model 114 7.2.1 Governing Equations 114 7.2.2 Boundary Conditions 114 7.2.3 Numerical Solution 115 7.3 Results and Discussion 118 7.4 Conclusions 127 Chapter 8 Analysis of Thermal Comfor t Enhancement by Using Ceiling Fan in AirConditioned Residential Room 129 8.1 Problem Description 129 8.2 Computational Model 131
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iii8.2.1 Governing Equations 131 8.2.2 Boundary Conditions 132 8.2.3 Numerical Solution 133 8.3 Results and Discussion 135 8.4 Conclusions 145 Chapter 9 ThreeDimensional Analysis of Thermal Comfort and Contaminant Removal in Hospital Operating Room 147 9.1 Problem Description 147 9.2 Computational Model 151 9.2.1 Governing Equations 151 9.2.2 Boundary Conditions 152 9.2.3 Numerical Solution 153 9.3 Results and Discussion 156 9.4 Conclusions 172 Chapter 10 A Guideline on Using CFD for Indoor Space Modeling 173 10.1 Introduction 173 10.2 Creating the Geometry and Meshing 175 10.2.1 Mesh Development for 2D Model 178 10.2.2 Mesh Development for 3D Model 182 10.3 Specifying Physics Settings 187 10.3.1 Governing Equations and Physical Properties 187 10.3.2 Turbulence Modeling 188 10.3.3 Boundary Conditions 189 10.4 Solving the Model 190 10.5 Postprocessing and Visualization 191 Chapter 11 Conclusions 193 11.1 Numerical Modeling and Simulati on of Heat and Mass Transfer 193 11.2 Future Works 199 References 202 Bibliography 209 Appendices 211 Appendix A: FIDAP Subroutine for Co mputation of Relative Humidity 212 Appendix B: FIDAP Preprocessing Input for Chapter 3 213 B.1 Geometry and Meshing: FIDAP Commands 213 B.2 Simulation Settings : FIDAP Commands 218 Appendix C: FIDAP Preprocessing Input for Chapter 4 220 C.1 Geometry and Meshing: FIDAP Commands 220 C.2 Simulation Settings : FIDAP Commands 225 Appendix D: GAMBIT/FIDAP Prep rocessing Input for Chapter 5 228
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ivD.1 Geometry and Meshing: GAMBIT Commands 228 D.2 Simulation Settings : FIDAP Commands 239 Appendix E: GAMBIT/FIDAP Prep rocessing Input for Chapter 6 242 E.1 Geometry and Meshing: GAMBIT Commands 242 E.2 Simulation Settings : FIDAP Commands 244 Appendix F: GAMBIT/FIDAP Prep rocessing Input for Chapter 7 247 F.1 Geometry and Meshing for 2D Model: GAMBIT Commands 247 F.2 Simulation Settings for 2D Model: FIDAP Commands 254 F.3 Geometry and Meshing for 3D Model: GAMBIT Commands 257 F.4 Simulation Settings for 3D Model: FIDAP Commands 270 Appendix G: FIDAP Preprocessing Input for Chapter 8 273 G.1 Geometry and Meshing: FIDAP Commands 273 G.2 Simulation Settings : FIDAP Commands 288 Appendix H: GAMBIT/FIDAP Prep rocessing Input for Chapter 9 291 H.1 Geometry and Meshing: GAMBIT Commands 291 H.2 Simulation Settings : FIDAP Commands 302 Appendix I: MATLAB Programs fo r 3D Solution Visualization 306 I.1 Import Numerical Solution from FIDAP 306 I.2 Solution Visualization for 3D Operating Room (Chapter 9) 307 About the Author End Page
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v List of Tables Table 2.1 Summary of problems under study 30 Table 3.1 Numerical values of fixed dimensions in Figure 3.2 33 Table 3.2 Simulation cases for storage tank with nozzle head 35 Table 4.1 Numerical values of fixed dimensions in Figure 4.2b 56 Table 4.2 Simulation cases for storage ta nk with heat pipe and array of pumpnozzle units 56 Table 5.1 Numerical values of fixed dimensions in Figure 5.2b 78 Table 5.2 Simulation cases for storage ta nk with heat pipe and lateral pumpnozzle unit 78 Table 6.1 Numerical values of fixed dimensions in Figure 6.2b 95 Table 7.1 Numerical values of fi xed dimensions in Figure 7.2a 109 Table 7.2 Simulation cases for refrigerated warehouse 112 Table 7.3 Effects of cooling unit lo cation to temperature distribution 127 Table 8.1 Numerical values of fixed dimensions in Figure 8.2 131 Table 8.2 Simulation cases for airconditioned room with ceiling fan 131 Table 8.3 Comparison of temperature, re lative humidity, and PPD for thermal comfort 141 Table 8.4 Effect of fan normal air speed on mean air speed in room and around person 144 Table 9.1 Simulation cases and comparison of results 150
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vi List of Figures Figure 3.1 Schematic of cryogenic storag e system with inje ction nozzle head 34 Figure 3.2 Axisymmetric model and essential dimensions 34 Figure 3.3 Quadrilateralelement mesh for axisymmetric model of storage tank with arrays of injecti on nozzles on nozzle head 38 Figure 3.4 Distributions of velocity a nd temperature, simulation case 1 (base case) 43 Figure 3.5 Distributions of velocity a nd temperature, simulation case 5 (H* = 1.2) 43 Figure 3.6 Effect of depth of nozzle head on distributions of speed and temperature 45 Figure 3.7 Effect of span of nozzle head on distributions of speed and temperature 46 Figure 3.8 Effect of inlet diameter on distributions of speed and temperature 50 Figure 3.9 Effect of geometry setti ngs on wall temperature and local Nusselt number 51 Figure 3.10 Average Nusselt number as function of geometry setting 52 Figure 4.1 Schematic of cryogenic storag e system with polar array of pumpnozzle units 55 Figure 4.2 Threedimensional domain and simplified axisymmetric model 55 Figure 4.3 Quadrilateralelement mesh for axisymmetric model of storage tank with heat pipe and polar array of pumpnozzle units 59 Figure 4.4 Distribution of ve locity, pressure, and temperature, simulation case 1 63 Figure 4.5 Effect of speed at nozzle and spraying gap on speed distribution 66
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viiFigure 4.6 Effect of speed at nozzle and spraying gap on temperature distribution 66 Figure 4.7 Effect of length of heat pipe on average speed and maximum temperature 68 Figure 4.8 Effect of length of inle t tube on average speed and maximum temperature 70 Figure 4.9 Wall temperature and Nusselt number, base geometry setting 72 Figure 4.10 Wall temperature and Nusselt number, Re = 21500 73 Figure 4.11 Average Nusselt number as function of Reynolds number 74 Figure 5.1 Schematic of cryogenic storag e system with single lateral pumpnozzle unit 77 Figure 5.2 Computational model and dimensions 77 Figure 5.3 Hexahedralelement mesh for 3D model of storage tank with heat pipe and lateral pumpnozzle unit 81 Figure 5.4 Velocity distribution, m/s, simulation case 1 85 Figure 5.5 Temperature distri bution, K, simulation case 1 86 Figure 5.6 Comparison of temperature distribution on symmetric plane, K 89 Figure 5.7 Effect of fluid speed at nozzle face on average speed 89 Figure 5.8 Effect of fluid speed at no zzle face on maximumaverage temperature difference 90 Figure 5.9 Effect of fluid speed at nozzle face on maximum temperature 90 Figure 6.1 Schematic of cryogenic storag e system with axial pumpnozzle unit 96 Figure 6.2 Threedimensional domain and simplified axisymmetric model 96 Figure 6.3 Quadrilateralelement mesh for axisymmetric model of storage tank with heat pipe and axial pump nozzle unit 98 Figure 6.4 Distribution of temper ature at the end of stage 1, K 100 Figure 6.5 Maximum and mean temper atures vs. elapsed time, stage 1 100
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viiiFigure 6.6 Distributions of velocity and temperature, stage 2, 5 minutes 102 Figure 6.7 Distributions of velocity and temperature, stage 2, 60 minutes 102 Figure 6.8 Maximum and mean temper atures vs. elapsed time, stage 2 103 Figure 6.9 Distribution of temper ature at the end of stage 3, K 106 Figure 6.10 Maximum and mean temper atures vs. elapsed time, stage 3 106 Figure 6.11 Maximum and mean temperature vs. elapsed time for first 3 cycles 107 Figure 7.1 Basic arrangement in a refrigerated warehouse 110 Figure 7.2 Twoand threedimensional models for refrigerated warehouse 111 Figure 7.3 Quadrilateralelement mesh fo r 2D model of refrigerated warehouse with cooling unit and packages 116 Figure 7.4 Hexahedralelement mesh fo r 3D model of refrigerated warehouse with cooling unit and packages 117 Figure 7.5 Distributions of air velocity, pressure, and temperature for simulation case 1 (3D model, base case: X = 1.1 m, Z = 3.3 m) 121 Figure 7.6 Distributions of air velocity, pressure, and temperature for simulation case 2 (2D model, base case: X = 1.1 m, Z = 3.3 m) 124 Figure 7.7 Effects of blowing air speed on temperature distribution 126 Figure 7.8 Effects of cooling unit location on temperature distribution 126 Figure 8.1 Residential room with air conditioner and ceiling fan 130 Figure 8.2 Twodimensional model of airconditioned room with ceiling fan 130 Figure 8.3 Quadrilateralelement mesh fo r 2D model of room with person and ceiling fan 134 Figure 8.4 Distributions of velocity, temperature, and relative humidity for simulation case 1 138 Figure 8.5 Distributions of velocity, temperature, and relative humidity for simulation case 2 138
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ixFigure 8.6 Comparison of PMV distribu tion between simulation cases 1 and 2 140 Figure 8.7 Effect of fan normal air speed on mean temperature 143 Figure 8.8 Effect of fan norma l air speed on thermal comfort 143 Figure 9.1 Threedimensional m odel of hospital operating room 149 Figure 9.2 Hexahedralelement mesh fo r 3D model of hosp ital operating room 155 Figure 9.3 Distributions of air velocit y, pressure, contaminant concentration, temperature, and relative hu midity for simulation 1 ( YS = 1.5 m, YE = 1.5 m) 157 Figure 9.4 Distributions of air velocit y, pressure, contaminant concentration, temperature, and relative hu midity for simulation 3 ( YS = 0.5 m, YE = 1.5 m) 162 Figure 9.5 Comparison of air flow patte rns from simulations cases 1 and 3 165 Figure 9.6 Mean contaminant c oncentration as function of YS and YE 169 Figure 9.7 CRE as function of YS and YE 169 Figure 9.8 PMV for patient as function of YS and YE 170 Figure 9.9 PMV for staff me mber 1 as function of YS and YE 170 Figure 9.10 PMV for staff me mber 2 as function of YS and YE 171 Figure 9.11 PMV for staff me mber 3 as function of YS and YE 171 Figure 10.1 Geometry decomposition and meshing for 2D model 181 Figure 10.2 Geometry decomposition for 3D model using encapsulation technique 184 Figure 10.3 Hexahedral mesh for 3D model using encapsulation technique 185 Figure 10.4 Refined mesh in transition zones and regul ar mesh in global space 186
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x List of Symbols C average contaminant concentration, kg/kg air c contaminant concentration in air mixture, kg/kg air cp specific heat, J.kg .K CRE contaminant removal effectiveness D mass diffusion coefficient, m/s dh hydraulic diameter, m fcl ratio of clothed surface area to nude surface area G source of heat generation per unit of volume, W/m g gravitational acceleration, m/s h enthalpy, J/kg; heat tran sfer coefficient, W.m .K Icl thermal resistance of clothing in clo units, clo k thermal conductivity, W.m .K lc characteristic length scale of the flow, m lm mixing length, m ln distance from the nearest wall, m M metabolic heat production, W/m n normal direction Nu Nusselt number p pressure, Pa
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xi PMV predicted mean vote PPD predicted percent dissatisfied Pr Prandtl number q heat flux, W/m r r direction Rcl thermal resistance of clothing, m.K/W Re Reynolds number RH relative humidity S generatrix total length s arc length coordinate, m T temperature, K (liquid hydrogen) or C (air) t time, s U fluid speed, m/s u velocity, m/s v air velocity, m/s V prescribed velocity, m/s W external work accomplished, W/m w water vapor concentration in air mixture, kg/kg air X parametric distance in x direction, m x x coordinate, m Xi body force per unit of volume in i direction, N/m, xi generalized spatial coordi nates in tensor notation, m Y parametric distance in y direction, m
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xii y y coordinate Z parametric distance in z direction, m z z coordinate Greek symbols growth ratio of element layers in mesh transition zone thermal expansion coefficient, K nominal mesh size, m ij Kronecker delta function u relative error tolerance R residual tolerance height of mesh transition zone, m von Krmn constant dynamic viscosity, Pa.s number of element layers in mesh transition zone Lam's constant density, kg/m ij viscous shear stress tensor, N/m species concentration, kg/kg air general boundary Subscripts a air, air mixture amb ambient air
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xiii body on body surface BZ breathing zone c/a of contaminant in air mixture CF concrete floor cl of clothed body or clothing conv convection cool cooling E exhaust gnd ground i i direction, tensor index, i th iteration j j direction, tensor index k species k in a mixture, tensor index lampface on front surface of light set lampback on back cover of light set light lightings patient on patient outer surface PU polyurethane rad radiation, radiant ref reference S supply s solid (product packages) staff on staff member outer surface supply on supply opening
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xiv t turbulent or eddy w water vapor w/a of water vapor in air mixture wall at wall ws saturated water vapor Superscripts dimensionless parameter
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xv Numerical Modeling and Simula tion for Analysis of Convective Heat and Mass Transfer in Cryogenic Liquid Storage and HVAC&R Applications Son Hong Ho ABSTRACT This work presents the use of numerical modeling and simulation for the analysis of transport phenomena in engineering syst ems including zero boiloff (ZBO) cryogenic storage tanks for liquid hydr ogen, refrigerated warehouses and humanoccupied airconditioned spaces. Seven problems of medium la rge spaces in these fields are presented. Numerical models were develope d and used for the simulation of fluid flow and heat and mass transfer for these problems. Governing equations representing the conservation of mass, momentum, and energy were solved num erically resulting in the solution of velocity, pressure, temperature, and species concentration(s). Nume rical solutions were presented as 2D and 3D plots that provide more insightful understanding of the relevant transport phenomena. Parametric studie s on geometric dimensions and/or boundary conditions were carried out. Four designs of ZBO cryogeni c liquid hydrogen storage tank were studied for their thermal performan ce under heat leak from the surroundings. Steady state analyses show that higher flow rate of forced fluid flow yiel ds lower maximum fluid temperature. 3D simulation provides the visual ization of the complex structures of the 3D distributions of the fluid ve locity and temperature. Transient analysis results in the patterns of fluid velocity and temperature fo r various stages of a proposed cooling cycle and the prediction of its effec tive operating term. A typical refrigerated warehouse with a
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xvi set of ceiling type cooling units were m odeled and simulated with both 2D and 3D models. It was found that if the cooling units are closer to the stack s of stored packages, lower and more uniform temperature distri bution can be achieved. The enhancement of thermal comfort in an airconditioned reside ntial room by using a ceiling fan was studied and quantified to show that thermal comfort at higher temperature can be improved with the use of ceiling fan. A 3D model was used for an analysis of thermal comfort and contaminant removal in a hospital operating room. It was found that if the wall supply grilles are closer to the center, the system has better performance in both contaminant removal and thermal comfort. A practical guideline for using CFD modeling in indoor spaces with an effective meshi ng approach is also proposed.
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1 Chapter 1 Introduction 1.1 Cryogenic Liquid Hydrogen Storage Hydrogen has been well recognized as a pow erful and clean energy fuel for a few decades, especially for space applications such as the Centaur upper stage rocket (Dawson and Bowles, 2004). Although hydroge n has many advantages over most conventional fuels, efficient storing of hydr ogen is difficult because of its very low density (Colozza, 2002). Besides severa l new devising storage methods (carbon nanotubes, carbon fullerenes, and hydrides), conventional methods in which hydrogen is stored as a compressed gas or as a cryoge nic liquid are still two primary storage techniques used in the in dustry. Liquid storage of hydrogen has a very significant advantage over gaseous or ch emical storage because of its much lower storage volume and ease of regeneration of the fuel with its demand. Conventional cryogenic storage tanks suffer loss of hydrogen due to boiloff of the cryogen induced by heat leak to the tank from the surrounding environment. In orde r to keep the inner pressure within the structural limits of the tank, the stored fluid needs to be periodically vented. The Zero BoilOff (ZBO) concept has evol ved as an innovative means of storage tank pressure control by a synergistic applic ation of passive insu lation, active heat removal, and forced mixing within the tank. The goal is that the fuel can be stored for a very long time with almost no loss. In recent years, a number of efforts have been done towards the guidelines of building cryogenic st orage systems, especially with the ZBO
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2 concept. Salerno and Kittel (1999) presen ted the proposed Mars reference mission and the concomitant cryogenic fluid management technology with a combination of both active and passive technologies to satisfy a wide range of requirements. Kamiya et al. (2000, 2001) consecutively presente d the development of a larg e experimental apparatus to measure the thermal conductance of various in sulations and used that for the testing of insulation structures. Hasting et al. (2002) presented an overview of the efforts in the development of the ZBO storage systems at NASA, showing that a ZBO system has mass advantage over passive storage. Kittel (2002) suggested an alternative approach for the longterm storage of cryogenic propellants us ing a reliquefier that uses the propellant vapor as the working fluid. Khemis et al. ( 2003) presented an experi mental investigation of heat transfer in a cryost at without lateral insulation. Panzarella and Kassemi (2003) presented a comprehensive analysis of the transport processes that control the selfpressurization of a cryogenic tank in normal gravity. Hofmann (2004) presented a theory of boiloff gascooled shields for cryogenic st orage vessels using an analytical method to determine the effectiveness of intermediate refrigeration. Haberbusch et al. (2004) developed a design tool for thermally zero boi loff densified cryogen storage system for space. The model predicted that a ZBO densified liquid hydrogen storage system minimizes the overall storage system mass a nd volume for nearly the same input power for cooling. Mukka and Rahman (2004a, 2004b) used computational fluid dynamics (CFD) simulation to study the fluid flow and heat transfer in a cryogenic liquid hydrogen storage tank of displacement type where cool fluid enters the tank at one end, mixes with hot fluid inside, and exits at the other end. Mahmoud et al. (2004) presented the modeling of the amount of liquid parahydrogen vapor ized during a discharging/charging process
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3 in a cryogenic storage system. Venkat and Sh erif (2004) studied a liquid storage system under normal and reducedgravity conditions. Li et al. (2004) analy zed the effects of liquid volume fraction, temperat ure, and pressure on the pres sure rise rates in cryogenic vessels. Reiss (2004, 2006a, 2006b) presented numerical simulations, using thermal networks, of shield temperature and radi ative and conductive heat losses of a superinsulated cryogenic storage tank operating at 77 K in stationary and unsteadystate conditions. Plachta et al. (2006) presented the propellant storage thermal analysis and design for two space missions. They modeled and designed passive storage concepts for cryogenic propellants for these missions. The prope llant tanks view was isolated to deep space to achieve zero boiloff for both liqui d hydrogen and liquid oxygen storage without cryocooler. The ZBO concept for cryogenic liquid stor age has been developing recently for less than ten years. A number of study has b een done are experimental. On the side of theory development, modeling, and simulation, mo st of the analysis work has been done using energy balance (thermodynamics approach ) or simplified theories for design. These studies confirm the feasibili ty of the ZBO concept in cryogenic liquid storage in macroscopic level. Transient analyses are also reported for some unsteady processes. Although CFD method has many adva ntages over the other me thods, especially that it allows the study of the distribu tions of temperature and fluid flow in details and thus gives insightful understanding of the transport phenomena, the use of CFD approach in the field is in its first developing phase. A few works using CFD simulation have been done for some tank designs under different wo rking environments. The results reported are mostly the distributions of fluid flow a nd temperature in details. Most CFD analysis
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4 work employs axisymmetric models. Explicit predictions on the effects of forced fluid velocity and geometric dimensions as design pa rameters on the distributions of fluid flow and temperature, and thus overall thermal pe rformance of the system, of a ZBO storage tank design have not been focused adequately and studied systematically. Complex 3D patterns of fluid flow and temperature in a ZBO storage tank are necessary to understand the transport phenomena and need to be done. Fo r an investigation of the effectiveness of a cooling cycle in ZBO storage tank, maximum temperature is the key parameter since it triggers the boiloff of the fluid in the ta nk. A transient analysis for studying a cooling cycle controlled by maximum flui d temperature is necessary. Chapters 3 through 6 propose four desi gns for ZBO cryogenic liquid hydrogen storage system. Chapter 3 presents a steadystate an alysis for liquid hydrogen inside a storage tank equipped with an in let tube and a nozzle head th at contains many nozzles on its front face. Liquid hydrogen cooled by an external cryocooler flows along the nozzle head assembly, penetrates into the bulk liqui d through the nozzles in order to prevent the boiling off due to heat leak from the surr oundings through the tank wall insulation, exits the tank through an annular outle t opening coaxial w ith the inlet, and then goes back to the external cooling system. This design was proposed by Ho and Rahman (2006). The design concept was similar to that of a test prototype developed at NASA Glenn Research Center presented by Hedayat et al. (2002). Th e prototype had a spray bar located along the centerline and the fluid in the tank was drawn through a nearby opening instead of nozzle head and concentric ou tlet opening in the present de sign. A parametric analysis was performed for different geometric setti ngs to find the best dimensions for an optimized design.
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5Chapter 4 presents a steadystate analys is for liquid hydrogen inside a storage tank with a heat pipe and an array of pumpnozzle units distributed around the heat pipe that creates a forced flow directed onto the ev aporator section of the heat pipe in order to prevent the liquid from boiling off due to he at leaking through the tank wall insulation from the surroundings. This design was proposed by Rahman and Ho (2005). The heat pipemixer (pump) design concept was firs t introduced by Plachta (2004) as another ZBO design concept implemented by a protot ype developed at NAS A Glenn Research Center. The prototype had a h eat pipe with many fins on th e evaporator section and a mixer pump that collected and directed the fl uid toward the heat pipe fins. The present design has smooth evaporator section of th e heat pipe and lateral pumpnozzle units. Parametric analysis was performed for both geom etric settings and fluid velocity from the nozzle. Chapter 5 presents a steadystate analys is with a 3D model for liquid hydrogen inside a storage tank equipped with heat pi pe and a single lateral pumpnozzle unit that collects fluid at its inlet and discharges through its nozzle onto the evap orator section of the heat pipe in order to pr event the fluid to boil off due to the heat leaking through the tank wall from the surroundings. This design was proposed by Ho and Rahman (2007b). It is similar to the previo us design but only has on pump nozzle unit that make the geometry of the tank highly 3D and complex, and so are the fluid flow and temperature distribution. The 3D simulation provides the complex 3D solu tion of interest such as velocity and temperature inside the tank. Chapter 6 presents the tran sient analysis for liquid hydrogen inside a storage tank with a heat pipe located al ong the symmetric axis of the tank, and an axial pumpnozzle
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6 unit that collects fluid inside the tank and discharges onto th e evaporator section of the heat pipe, which is kept at a constant lo w temperature, where the heat is removed passively to the condenser section of the heat pipe located outside th e tank and eventually to the ambient via an active cryocooler. This design was proposed by Ho and Rahman (2007a). It is closely similar to the protot ype presented by Plachta (2004) except that the prototype had no nozzle and the pump mixer wa s not axisymmetric. A transient analysis using CFD approach was performed. The distribu tion of fluid velocity and temperature in different cooling stages and the effective lifetime of a cooling scheme were studied. 1.2 Refrigerated Warehousing The utilization of refrigeration for the co ld storage of perishable foods has been employed for more than a century. The needs for refrigerated storage grow with hot weather. The frozen food industry has expa nded many times in freezer storage in a few decades after World War II. Recently, the gro ss capacity of refrigerated warehouses in the United States has increased constan tly every year. Indus trial refrigeration applications, specifically refr igerated warehouses, are also significant energy consumers. Proper design of space for refrigeration require s knowledge of thermal behavior of the air distribution and thermal conditions within the space. Cold storage facilities require the most attention to thermal behavior since it gr eatly influences the cost. Many refrigerated spaces operate at low temperatures, which incr ease the severity of the service condition imposed on the system. Frozen food quality is sensitive to both storage temperature and fluctuations in temperature. Inadequate re frigeration system operation may result in negative impacts on product quality: accelerated deterioration reactions at elevated temperatures, the growth in ice crystal size occurring during the temp erature fluctuations.
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7 Even for a thermally well insulated refriger ated warehouse with no loading or unloading activities, there is still heat transfer through floor, ceiling, and walls, as well as heat load from lighting. Cooling units (CU) such as those equipped with cooling coil and blowing fan have to be employed to keep the food products under proper temperature. Ceiling type cooling units are used frequently in larger cold storage rooms, both freezer and cooler, because they are out of the way and use no valuable floor space and are also high enough off the floor that they are not subj ect to damage from materials handling equipment (Woolrich and Hallowell, 1970). In a ceiling type CU, direct mounted fans of propeller type either blow th rough the coil bank or placed on the outlet side and pull the air through the coil bank. Guidelines of settings in a refrigerat ed warehouse can be found in several books such as International Institute of Refr igeration (IIR, 1966), W oolrich and Hallowell (1970), Tressler et al. (1968), and Hardenbur g et al. (1986). The ma nual by Woolrich and Hallowell (1970) provides a comprehensib le background and common practice on refrigerated warehouse construction, equi pment, and management. More specific guidelines for preservation of foods can be f ound in Tressler et al. (1968). Theoretically, frozen food should be stacked in solid piles in such a way as to reduce to the minimum air circulation around the products for keepi ng less desiccation and oxidation except for the case that the products are canned or packed in sealed containe rs. Frozen foods are warehoused in a number of different types of containers including wooden boxes, fiber board containers, tin cans, etc. The guidelines by Tressler et al. ( 1968) suggest that for any types of storage containers used, the pack ages must be so placed in storage as to allow air circulation around them to improve cooling effectiveness. For maintaining
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8 vertical circulation, the packag es should not be stacked too cl ose to the walls. A clearance of 6 in. (0.15 m) or more should be provided on all four sides of the storage room. Aisles between arrays of stacks are needed, mainly for the handling operations but also for horizontal circulation. The width of the aisles should be considered to allow the use of mechanical loading equipments while saving storage space. Packages should not be piled higher than 12 to 18 in. (0.30 to 0.46 m) be low the ceiling or 6 in. (0.15 m) below the bottom of the ceiling coils and should not be stacked within 5 feet (1.52 m) of any nonrefrigerated space, such as openings to stairs or elevator wells. Packages of frozen food should never be stocked direc tly on the floor but may be p iled on forktype pallets or on floor racks at preferably 4 in. (0.10 m) above the floor. General use of pallets improves the organization of refrigerated transport, and pallets can se rve as floor dunnage at the same time. The practice guide by the IIR (1966) provides more specific guidelines on the use of pallets in refrigerated warehouses. A clearance of 2 to 6 in. (0.05 to 0.15 m) width on each side of the pallet is necessary to provide a free space of 4 to 12 in. (0.10 to 0.30 m) between two pallets to reduce the difficulty of placing and remova l of pallets as well as to induce vert ical circulation. Although there are general gu idelines of operation of refrigerated warehouses, they do not show how relevant parameters affect the cooling effectiveness and temperature uniformity for refrigerated warehous e. Therefore, more studies in details are needed to evaluate the effectiveness of the combinations of parameters on efficiently utilizing them in various situations, fo r both design and operation of refrigerated warehouse. Baird and Gaffney (1976) deve loped a numerical model for predicting transient heat transfer in precooling operation. The numerical model and procedures
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9 allowed calculations of cooling rates in beds of fruits and vegetables as a function of product size, air velocity, air temperature, and depth of the bulk load. Later, Baird et al. (1988) proposed the design criteria for effici ent and cost effective forced air cooling systems for fruits and vegetables which cove r the effects of many parameters including initial product temperature, desired final pr oduct temperature, flow rate, temperature and relative humidity of the coo ling air, ambient temperature, etc., among other factors related to characteristics of product and equipment, and cost. An engineeringeconomic model was used to study the influence of each of these variables as well as some of their interactions as they affect cooling time a nd/or cooling cost. Ni coulin et al. (1997) presented the use of generalpurpose transien t simulation computer models for simulating the energy performance of large commercial refrigeration systems typically found in food processing facilities to predict facility perf ormance and estimate savi ngs with inclusion of modeling issues specific to refrigerated warehouse systems, including warehouse loading door infiltration calculations, evaporator m odel, singlestage and multistage compressor models, evaporative condenser models and defrost energy requirements. The increasing developments of computer s and the field of computational fluid dynamics (CFD) in the recent years have ope ned the possibilities of a lowcost yet effective method for modeling and simulation of airflow and heat transf er in refrigerated warehouses with fewer physical experiments required. Smale et al. (2006) reviewed various numerical modeling techniques, focu sing on CFD and briefly on others including Lattice Boltzmann method (LBM) and network m odels, to the prediction of airflow in refrigerated food applications including cool stores, tr ansport equipment and retail display cabinets. Hoang et al. ( 2000) presented an analysis of airflow in a cold store using
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10 CFD approach employing the Reynoldsave raged NavierStokes equations with k turbulence model. A comparison with experiment al measurements resulted in an average difference of 26% between calculated and meas ured air velocities. Nahor et al. (2005) developed a transient threedimensional CFD model with the use of standard k turbulence model to calculate the velocity, temperature and moisture distribution in an existing empty and loaded cool store. The re sults showed that an average accuracy of 20%22% on the velocity magnitudes was ach ieved and that the model was capable of predicting both the air and product temperatur e with reasonable accuracy. Chourasia and Goswami (2007) simulated the effects of st ack dimensions and stacking arrangements on heat transfer characteristics in a stack of bagged potatoes during cooling by using a CFD model and found a satisfactory agreement between the experimental transient temperature data from a commercial potato cold store and simulated results with an average temperature difference of 1.4 0.98C. Fo ster et al. (2002, 2003, 2006, 2007) reported several studies concerned with reducing air infiltration in cold stores by means of CFD modeling and simulation for various cases. A CFD model for air movement through a doorway was developed and veri fied against conventional an d laser Doppler anemometry (LDA) measurements (Foster et al., 2002). Meas urements of infiltration through different size entrances of a cold store at two differe nt cold store temperatures were taken and compared against established analytical m odels and CFD models (Foster et al., 2003). More recently, they presented 2D and 3D anal ysis of the effectiveness and optimization of air curtain devices with CFD models and comparison to the measured data (Foster et al., 2006, 2007). For each study, the CFD model wa s generally found to be in agreement with experimental data to some degrees. The effects of the relative position of a cooling
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11 unit to the stacks of product packages to the distribution of temperature within a large refrigerated space is important to designi ng a new warehouse or managing an existing one to allow the use of the refrigerated sp aces effectively. This aspect has never been addressed. It is the aim of the study in Chapter 7 to find an optimum location for the cooling unit relative to stacks of product packages in a refrigerated warehouse. Chapter 7 presents an analysis of steadystate thermal behavior in a refrigerated warehouse equipped with ceilingtype cooling units. The computational domain includes a refrigerated space with arrays of 2 backtoback rows of 4 piles by 3 stacks of palletized product packages. On the ceiling in front of them is installed a set of cooling units where the fan pulls air through cooling coil and blow s into the space. Both 3D and 2D models were employed for studying the transport phe nomena. 2D model was then employed for a parametric analysis to study the effects on temperature of va rious blowing air velocities and different locations of the cooling unit( s). The maximum and av erage temperature and the spatial standard deviation of temperatur e distribution were employed for quantitative assessment on the effects of the cooling unit lo cations to the temperature distribution in the refrigerated warehouse. 1.3 Indoor Environment Control Thermal comfort is dependent on many fact ors, in which temperature, humidity, and air speed are among the most important ones. For a cooling scenario, although low temperature is the first choice for comfort c ontrol, moderate air speed as a breeze can enhance thermal comfort at higher temperatur e by wind chill effect. In residences, temperature control is achieved by using air conditioners, while air speed can be increased by using ceiling fans. The proper use of a ceiling fan in an airconditioned
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12 room can result in better thermal comfort a nd energy savings. Rohles et al. (1982, 1983) have studied the effectiveness of ceiling fa ns in enhancing comfort experimentally by examining 256 subjects under various temperat ure and air velocity in an environment chamber equipped with a ceiling fan. The result s showed that an air plume from a ceiling fan whose velocity is between 0.51.0 m/s compensates for a 2.83.3C temperature change; this represents an energy savings of 1518%. MortonGibson et al. (1985) have investigated the effects of ceiling fans or i ndividual fans on therma l comfort in an office building and found that operating fans for a bout 1000 hours per year at 26.7C results in approximately the same comfort levels as 24.4C without fans and that the resulting savings are more than the cost and energy us age of the fans. James et al. (1996) have presented a simulation study using energy balan ce approach to show the relationship of residential cooling energy use to interior thermostat set points and fan use. This study considered 400 Florida households. It is f ound that significant cooling energy use savings are possible if ceiling fans are used with high er thermostat set point s. In this field, the work has been done mostly employs experime ntal and energy balance approaches. CFD simulations are needed for more details of th e distribution of veloci ty, temperature, and humidity in the space to pr edict human thermal comfort mo re accurately. A CFD solution is very detailed as it distribut es over the entire space of intere st. It can be advantageous to use only parts of the numerical solution within a small zone that encloses the human body model to predict thermal comfort, rather than using the solution in the entire space. This allows the predictions of thermal comfort closer to the condit ion of the human body. Chapter 8 presents an analysis on airflow and heat transfer in a residential airconditioned room with a ceili ng fan. The room model includes a person standing in the
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13 middle of the room, under the cei ling fan and a light set attached to it. Cold air is supplied to the room through high sidewall grilles and exhausted through lo w sidewall grilles on the opposite wall. The distributions of velocit y, temperature, and humidity in the room were expected to provide a detailed description of the transport phenomena that took place in the space of interest. Thermal comfor t was estimated for one case with no ceiling fan and three other cases with different fan nor mal air speed for a parametric analysis to show the effect of using ceiling fan on therma l comfort. The effects of ceiling fan to human thermal comfort and the difference of the predictions of thermal comfort in the local zone or the entire space were to explore. This work is the first one that uses CFD simulation to model fluid flow and heat transf er and to predict human thermal comfort in indoor space with ceiling fan. Health care facilities, machine shops, manufacturing and chemical processing facilities, and other commercial occupancies require ventilation and air conditioning for thermal comfort as well as for the removal of contaminants and other pollutions. A good design of ventilation and ai r conditioning system provide s a healthy and comfortable environment for patients, workers, and visito rs. Poorly ventilated workspaces not only make people feel uncomfortable but also incr ease the risk of getti ng people infected or intoxicated since the concentr ation of air borne pathogens or other kinds of toxic chemicals can be high. The design of a H eating, Ventilating, and AirConditioning (HVAC) system for an operating room aims to prevent the risk of infections during surgical operations while maintaining an ad equate comfort condition for the patient and the surgical staff. Proper indoor comfort condi tion and indoor air quality are prerequisites for securing a safe and suitable environment for an operating room. There are standards
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14 to guide the design of airconditioning systems for operating rooms around the world among which the American Institute of Ar chitects has guidelines (AIA, 2001) for the design and construction of hospita ls and health care facilitie s. On HVAC design point of view, The American Society of Heating, Refrigerating and AirConditioning Engineers (ASHRAE, 1995) recommends gene ral guidelines for an operating room as follows: that temperature should be kept in the range of 68F (20C), that relativity humidity should be kept between 50% and 60%, that pos itive air pressure should be maintained, and that all air exhausted with no recirculation is preferred. A number of experimental studies have been presented a bout infections and related factors in operating room s. Woods et al. (1986) presente d a project to identify and demonstrate control strategies that coul d reduce energy requirements whereas not producing harmful effects on the environmenta l quality within the operating room. The project was done through extens ive literature search, develo pment of mathematical and biophysical models, and analysis of data obtained in two ex isting operating rooms with different system performance characteristics. Lewis (1993) studied the influence of room air distribution on the infection rate in an operating room and concluded that air distribution plays an important role in ma intaining the proper e nvironmental condition within a surgical room. Conve ntional operating room HVAC distribution systems may be entirely satisfactory when properly designed, balanced, and maintained if postoperative infection is not a significant problem. More effective air di stribution will be justified when the infection problem has more severe c onsequences or results in a higher cost of treatment. Memarzadeh (2000) proposed a methodology for minimizing contamination risk from airborne organisms in hospital is olation rooms. The results show that the
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15 number of particles deposited on surfaces and ve nted out is greater in magnitude than the number killed by ultraviolet (UV) light, suggesting that ve ntilation plays an important role in controlling contaminant level. Me marzadeh and Manning (2003) presented an extensive study on operating room ventilation systems and their eff ect on the protection of the surgical site, focusing on preventing th e risk of postoperative infection from many factors including patient factors, surgical fi eld factors, room fact ors, and HVAC factors. Mora et al. (2001) studied thermal co mfort in operating rooms. The thermal environment was studied in two operating r ooms at a hospital. Thermal comfort was estimated based on the PMVPPD model (p roposed by Fanger, 1970; widely adopted; details can be found in the Fundamental s Handbook by ASHRAE, 2005) in addition to questionnaires. It was concluded that the onl y means to provide thermal comfort for the surgical staff was to eliminate or to minimize the heat transfer from the surgical lights. They suggested that more research is n eeded to evaluate an acceptable thermal environment in operating rooms. It can be obser ved that there is a n eed to predict ambient conditions within an operating room. Balara s et al. (2002) presen ted an overview of general design for acceptable indoor conditions related to HVAC systems in hospital operating rooms. Audits of 20 operating rooms at 10 hospitals were recorded covering a wide range of information on construction, ow nership, type and condi tion of HVAC and auxiliary systems. Data on the assessment of the indoor conditions from 560 medical personnel working insitu were also collected based on personnel que stionnaires. Kameel and Khalil (2003) proposed guidance to arch itectural and mechanical engineering designers to optimize the comfort and hygien e conditions with optimum energy utilizing efficiency for operating theatres. This guidan ce focused in assessing the influence of the
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16 architectural and mechanical design on the HVAC airside system design and consequentially on the air quality, hygiene level, and energy utilizati on. Later, Khalil and Kameel (2004) discussed on the balance be tween thermal comfort and air quality in healthcare facilities to optimize the Indoor Ai r Quality (IAQ) from the viewpoint of the air conditioning design. The increasing development of CFD in r ecent years have opened the possibilities of a lowcost yet effective method for improving HVAC system in the design phase, with fewer physical experiments required. Me marzadeh and Manning (2000) studied the performance of a ventilation system in a typical patient room using CFD modeling. They were able to predict the necessity of us ing baseboard heating in extreme weather conditions. In addition, the validation of vari ous supply air diffuser models gives useful guidelines on CFD modeling for HVAC applications. Hirnikel et al. (2002) investigated contaminant removal effectiveness (CRE) of three air distribution systems for a bar/restaurant by using CFD modeling. The CRE was considered for both particulate and carbon monoxide, which were used to represen t the environmental tobacco smoke (ETS), and for two different ventilation rates. The results showed that air flow direction can reduce peoples exposure to contaminants Memarzadeh and Manning (2002) simulated contaminant deposition in an operating room using CFD air flow modeling and showed that a laminar flow condition is the best ch oice for a ventilation system when contaminant deposition is considered. The contaminant considered in this simulation study was particletype squames, or skin scales, ar ound 10 microns in size, released from three locations in the room and tracked to dete rmine if they would impinge on either the surgical site or a back table. Kameel ( 2003) presented the use of a three dimensional
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17 timedependent CFD model to assess the ai r flow characteristics in different airconditioned spaces. It was found that the extracti on port location is a critical design factor and has a direct effect on heat removal effici ency and the energy efficiency at the airside of airconditioning systems. Chow and Yang ( 2003) used CFD analysis to simulate the temperature distribution, air flow pattern, and contaminant dispersion supported by observations and field measurements in a case study. They concluded that the application of CFD is useful to help understand the ad equacy of the ventila tion design in renovation planning to match uptodate engineeri ng standards. Cheong and Phua (2006) investigated the air flow a nd pollutant distribu tion patterns in a negative pressure isolation room by means of objective measurement and CFD modeling based on three ventilation strategies consisting of several combinations of two air supply diffusers or grilles and two extract grilles mounted on the ceiling or on the wall a bove the floor level. The results show that extraction at a low ve rtical level is very effective in removing pollutant at the human breathing zone as comp ared to extraction at ceiling level. Lee et al. (2007) studied the effects of air inlet types consisting of a wall jet and ceiling diffuser on the dispersion of contaminant concentra tions in an experimental room with no occupant and with an occupant model present. The results show that the air inlet type is an important physical determinant of th e distribution of airborne contaminant concentrations because different air inlet t ypes generate different airflow patterns and thus different spatial concentration patterns. CFD simulation give the nume rical solution of the variab les of interest (velocity, temperature, etc.), which is useful for understanding the transport phenomena and is a means for qualitative assessment of an indoor space but not enough to assist a successful
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18 design without a parametric study and additi onal analysis for optimization. Quantitative assessment is usually required for design optim ization. The use of techniques from other fields, such as experimental design, is need ed in the design proce ss. A particular HVAC application requires particular objectivities. For operating room s or health care facilities in general, thermal comfort and contaminant removal are the most important factors and need to be optimized considering both. Cr itical HVAC indoor space s such as operating rooms are designed traditionally based on the experience of the designer as well as the existing spaces that are al ready in successful operation. Although CFD simulation can provide the numerical solution, it cannot replace the experience of the designer. Thus, to make the use of CFD solution more useful such that it can partly compensate for the lack of experience in a designer, a systematic procedure for processing the results from the parametric studies to optim ize the design is needed. Chapter 9 presents a 3D analysis for stea dystate airflow and heat transfer in a hospital operating room. The room model includ es a patient lying on an operating table, four surgical staff members standing around, a nd surgical lights above the patient. Cold clean air is supplied to the room through hi gh sidewall grilles and exhausted through low sidewall grilles on the opposite wall. Effects of horizontal lo cations of supply and exhaust grilles on thermal comfort and contaminant removal were studied. General linear models (GLM) for thermal comfort and contaminant rem oval as functions of these locations were developed for design optimization. This demons trates a systematic procedure to employ the techniques needed for th e optimization of the design. Although the use of CFD simulation is exponentially increasing in recent years for various HVAC indoor space applications, th ere is a lack of guideline in setting up
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19 CFD models and running simulation for such applications. The recent version of the Handbook by ASHRAE (2005) only has an intro ductory guideline fo r the use of CFD method for indoor environmental modeling. A lthough CFD tools (softw are) are widely available nowadays, there are still difficulties in using them for a particular task. Among the basic steps to set up a CFD model, the firs t step of geometry creating and meshing is tedious and time consuming, especially the me shing part. An effective meshing strategy is of great importance to reduce the datap reparation stage, which can consume up to 80% or more of the laborhours requir ed (FIDAP Document ation, Fluent, 2005). Chapter 10 proposes a practical guideline for the use of CFD method in indoor spaces modeling as complementary to the introductory guideline given in the Handbook by ASHRAE (2005). The guideline focuses on the meshing with a systematic approach that allows the development of a mesh of high quality and high fl exibility. In addition, the mesh generation can be considered semi automatic, therefore reduce time and labor, which is important to the costeffectiveness. Basic and common practice of other steps in CFD modeling and simulation are also presente d. This guideline will help users who are new to CFD method get familiar with the field conveniently.
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20 Chapter 2 Computational Modeling and Simulation 2.1 Governing Equations To describe the fluid flow and heat and mass transfer phenomena inside a space of interest, it is necessary to determine the distributions of velocity, temperature, and species concentrations over the entire co mputational domain by solving the system of governing equations for the conservation of mass, momentum, and energy. The fluids considered in this work are liquid hydroge n for the problems involving cryogenic storage tanks and air for the problems involvi ng HVAC&R indoor spaces Liquid hydrogen in storage tank can be considered incompressible. For the problems presented in this work, the fluid is considered as incompressi ble and having constant properties. All the flows in these problems considered are turbulent by nature. To model the turbulent flow, Reynolds' time averaged equa tions are employed. Detailed explanations on the formulation of the governing equations and Reynolds decomposition approach for turbulence modeling can be found in White (19 91) and Kays et al. (2005). The general governing equations applicable for all the problems presented in this work are reviewed briefly in the following subsections. 2.1.1 Conservation of Mass The conservation of mass (equation of conti nuity) of a fluid can be written in the most general form as: 0 j ju x t (2.1)
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21 For an incompressible (constantdensity) fluid, Equation (2.1) can be rewritten as: 0 j jx u (2.2) For multicomponent fluid flows, if the di ffusivity of the species in the carrying fluid is a constant, the conservation of mass of a species can be written as: j j k k j k j kx x D x u t 2 (2.3) 2.1.2 Conservation of Momentum The conservation of momentum (NavierStokes equations) of a fluid in the most general form can be written as: i j ij i j i j iX x x p x u u t u (2.4) The general deformation law for a Newtoni an viscous fluid can be written as: i j j i ij k k ijx u x u x u (2.5) For a constantproperty fluid (constant density or incompressible and constant viscosity), with the use of Equations (2.2) and (2.5), Equation (2.4) can be rewritten as: i j j i i j i j iX x x u x p x u u t u 2 (2.6) If the body forces are negligible, Equation (2.6) becomes: j j i i j i j ix x u x p x u u t u 2 (2.7)
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22 The buoyancy effect, which is always significant in HVAC&R spaces, can be introduced into Equation (2.6) using the Boussinesq approximation as: ref 2T T g x x u x p x u u t ui j j i i j i j i (2.8) 2.1.3 Conservation of Energy Assuming that heat conduction follows F ourier's law, the conservation of energy of a fluid flow can be written as: G x u x T k x x p u t p x h u t hj i ij j j j j j j (2.9) Assuming that there is no heat generation, that the flow has low velocity such that the dissipation function is negligible, that th e pressuregradient term is negligible, and that density and thermal conductiv ity are constants, Equation (2.9) can be rewritten as: j j j j px x T k x T u t T c 2 (2.10) 2.1.4 Mixing Length Turbulence Model The mixing length model is a simple ye t effective turbulence model involving a single unknown parameter called the mixing le ngth or the mean free path for the mixing of turbulent fluid flow. The mixing length m odel works well for relatively simple flows such as wall boundarylayer flows, and jet and wake flows without requiring additional governing equation. For the problems under stud y in this work, this turbulence model can be employed on considering that the rather co mplex flow in the computational domain is composed by several regions of simple tu rbulent flows (wall bounda rylayer and jet) separated far enough that the transport and hist ory effects of turbulence are insignificant
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23 (FIDAP Documentation, Fluent 2005). Details on turbulence modeling can be found in Kays et al. (2005) and Rodi (1984). The effective viscosity can be written as: t 0 (2.11) The eddy viscosity can be written in general form (Rodi, 1984) as: j i i j j ix u x u x u l 2 m t (2.12) where c n m09 0 minl l l (2.13) Similarly, the effective therma l conductivity can be written as: t 0k k k (2.14) where t t p tPr c k (2.15) In Equations (2.11) and (2.14), is the von Krmn consta nt which usually takes the value of about 0.41 and Prt is the turbulent Prandtl num ber which usually takes the value of about 0.85 (Kays et al., 2005). 2.2 Boundary Conditions To define the problem completely, appr opriate boundary conditions are required on all boundaries of the computational domai n. The boundary conditions applicable for the problems presented in this wo rk may have the following forms. Prescribed velocity: 0V ui on (2.16) Prescribed temperature: 0T T on (2.17)
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24 Prescribed concentration: 0 j on (2.18) Prescribed heat flux: 0q n T k on (2.19) Prescribed mass flux: 0 ,j j jq n D on (2.20) Linear heat transfer: 0T T h n T k on (2.21) 2.3 Relevant Formulas for Indoor Environment For indoor environment modeling, relative humidity and models for the prediction of thermal comfort are of great importance. Re lative humidity can be used combined with temperature for a simple assessment of huma n thermal comfort in an existing space. The PMVPPD model (PMV: Predicted Mean Vote; PPD: Predicted Percent Dissatisfied) is widely used and accepted for design and field assessment of comfort condition. 2.3.1 Relative Humidity From the solution of the primary variable s in an HVAC simulation: temperature, pressure, and water vapor concentration, re lative humidity can be computed using the formulas given by ASHRAE (2005) as: ws wRH p p (2.22) where w w p p0.37802 0.62198 101325w (2.23) 15 273 ln 10 65459673 0 15 273 10 14452093 0 15 273 10 41764768 0 15 273 10 48640239 0 10 13914993 0 15 273 10 58002206 0 exp1 3 7 2 4 1 1 1 4 ws. T . T . T . T . T p (2.24)
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25 2.3.2 PMVPPD Model This model for prediction of thermal comfort is adopted by ASHRAE (2005) and is widely used in practice. The predicted mean vote (PMV) index is a parameter for the prediction of thermal comfort in an occupied zone based on conditions of metabolic rate, clothing, air speed besides temperature a nd humidity. The PMV can be computed using the formulas given by ASHRAE (2005) as: amb w w amb cl conv cl 4 rad 4 cl cl 834 0014 0 001 0 867 5 0173 0 15 58 42 0 001 0 007 0 733 5 05 3 15 273 15 273 10 96 3 028 0 036 0 exp 303 0 PMV T M p M . W M p W M . T T h f T T f W M M . (2.25) where amb cl conv cl 4 rad 4 cl cl 8 cl cl15 273 15 273 10 96 3 0275 0 7 35 T T h f T T f R W M . T (2.26) 5 0 25 0 amb cl 5 0 5 0 25 0 amb cl 25 0 amb cl conv1 12 38 2 1 12 1 12 38 2 38 2. . . .v T T v v T T T T h (2.27) clo 5 0 1 0 05 1 clo 5 0 2 0 0 1cl cl cl cl clI I . I I . f (2.28) cl cl155 0I R (2.29) The PMV index refers to the ASHRAE thermal sensation scale: +3 hot +2 warm +1 slightly warm 0 neutral
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26 slightly cool cool cold ANSI/ASHRAE Standard 55 (2004) recomm ends that the acceptable thermal environment for general comfort is 0.5 < PM V < 0.5. The predicted percent dissatisfied (PPD) can be estimated based on PMV usi ng the formula given by ASHRAE (2005) as: 2 4PMV 2179 0 PMV 03353 0 exp 95 100 PPD (2.30) 2.4 Numerical Solution Procedure For a problem under study, the governi ng equations and the boundary conditions are solved using the finite element method (F EM). In FEM, the computational domain is discretized into elements. In each element, velocity components, pressure, temperature, and species concentrations, if any, are a pproximated by using the Galerkin procedure (Fletcher, 1984) that leads to a set of algebraic equations that defines the discretized continuum. The finite element method has a long and successful history in the solution of engineering analysis problems. 2.4.1 Preprocessing and Solution Algorithms A mesh of small elements is required fo r a finite element solution. For problems involving fluid flow and heat and mass transfer due to the formation of boundary layers, several layers of regular elements of highe r density (finer mesh) need to be assigned along the fluidsolid interfaces where high rate s of momentum and heat transfer exist. Finer element mesh is also required at complex geometry boundaries for improving the accuracy of approximating curves by line segm ents. The distribution of element size in a computational domain is determined from a mesh independence study by systematically
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27 changing the mesh density in all space directions, both globa lly and locally, to obtain a mesh that can give solutions of acceptable accuracy. The FIGEN module of FIDAP (Fluent, 2005) and the software GAMBIT (Fluent, 2006) were used for geometric modeling and me sh generation. The mesh were designed such that it can accommodate changes of geometric parameters and capable for automatic meshing. The computational domain is alwa ys decomposed into several subdomains: Small subdomains that cover the fine r mesh regions and require special treatments and close inspections Large subdomains that cover most of the area of the computational domain and have simple geometry ready for automatic meshing with regular elements The FIPREP module of FIDAP (Fluent, 2005) was used for setting up the physics of the computational model (material propert ies, initial and boundary conditions, etc.), and the simulation control options (solution algorithm, convergence to lerances, etc.). The physicssetting step is straightforward. The application of the Galerkin fini teelement procedure to the governing equations results in a set of nonlinear algebraic equations presented in matrix form as: F u u K (2.31) where K is the global matrix u is the global vector of unknowns (ux, uy, uz, p, T,...) F is a vector of the effects of body forces and boundary conditions The residual is defined as: F u u K u R (2.32) If u is an exact solution, then R(u) should be zero.
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28 Equations (2.31) are nonlinear and have to be solved using iteration procedure. The fully coupled successive substitution ap proach and the segregated approach were used for solving the problems presented in this work. Fully coupled algorithms: all governing equations are solved in a simultaneous coupled manner. Successive substitution is a simple solving scheme using fully coupled approach. At an iteration i, the iteration computati on can be written as: F u u K 1 i i (2.33) The fully coupled successive substitution algorithm can be used for most of the axisymmetric or 2D problems. It has two c onvergence criteria: the re lative error criterion that checks if the relative error at an itera tion is less than a preset tolerance and the residual criterion that checks whether the ratio of the residual vector at an iteration to a reference residual vector is less than another preset tole rance. The convergence criteria can be written as: u i i i 1 1u u u (2.34) R i0u R u R (2.35) The sign represents a norm operator, usually the Euclidean norm. The iterative procedure is considered converged when both criteria are satisfied. For 3D models, the number of elements and nodal points are usually so large that the use of a fully coupled algorithm may requi re computing resources that exceed those available. In that case, the segregated algor ithm can be used (in some big size problems, this may be the only choice) with only th e relative error convergence criterion (2.34).
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29 The segregated solution algorithm avoids the direct formation of a global system matrix. Instead, in each iteration, only one unknown is solved for, while the other keep their previous values. The next iteration is used to solve for the next unknown. Due to its sequential and uncoupled nature, the segregated approach requires le ss disk storage but more iterations than the fully coupled appr oach. The formulation of the segregated algorithm is quite involved and can be found in FIDAP Documentation (Fluent, 2005). The FISOLV module of FIDAP (Fluent, 2005) was used to solve the set of finite element equations (2.31). 2.4.2 Postprocessing The FIPOST module of FIDAP was used fo r post processing. The solution for the primary variables (velocity, pre ssure, temperature, etc.) is available in the database file *.FDPOST. FIPOST was used directly for comp uting values such as mean values, fluxes, etc. of the variables of interest. FIPOST was also used to export the solution data into FIDAP neutral files (text files with predefined format to store FIDAP solution in human readable form, usually used for transf er FIDAP solution to another computing environment). For computing relative humidity in HVAC problems, the author has developed a FIDAP subroutine implementing Equations (2.22) to (2.24) in FORTRAN (Appendix A:). This subroutine was compiled and produ ced a customized function for FIDAP used for computing the distribution of relative humid ity based on the distributions of pressure, water vapor concentration, and temperature from the numerical solution. The technical computing program Matlab (The MathWorks, 2006) was used to compute and generate 2and 3D visualizati ons for the numerical solutions from FIDAP
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30 imported into MATLAB through the neutral files. The statisti cal analysis software SAS (SAS Institute, 2006) was used to compute the generalized linear models (GLM) in Chapter 9 2.5 Problems Under Study Seven problems reported in this work have their characteristics summarized in Table 2.1. They are presented in an order su ch that the difficulty from a computational point of view increases gradually. The menti oned difficulty is in the sense of that in setting up the model, time and computing resources required, or in handling the simulation process. Table 2.1 Summary of problems under study Problem # Chapter Fluid SystemModel Analysis Body force 1 3 Liquid hydrogenOpen Axisy mmetricSteadystate None 2 4 Liquid hydrogenClosedAxisy mmetricSteadystate None 3 5 Liquid hydrogenClosed3D Steadystate None 4 6 Liquid hydrogenClosedAxisymmetricTransient None 5 7 Air Closed2D, 3D Steadystate Buoyancy 6 8 Air, 1 species Open 2D Steadystate Buoyancy 7 9 Air, 2 species Open 3D Steadystate Buoyancy The computational difficulty for each problem appears in different aspects that can be simplified into the following rules: Multicomponent flows (problems 6 and 7) are more difficult than singlecomponent flows (problems 1)
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31 Closed systems (problems 2) are more difficult than open systems (problems 1, 6, and 7) 3D models (problems 3, 5, and 7) are more difficult than axisymmetric or 2D models (problems 1, 2, 4, 5, and 8) Transient analysis with largely different time steps between stages (problem 4) are more difficult than steadyst ate analyses (problems 1 and 5) Momentum equations with buoyancy for ce (problem 5) are more difficult than those without body force (problems 1)
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32 Chapter 3 Analysis of Heat Transfer in Cryogeni c Liquid Hydrogen Tank with Arrays of Injection Nozzles 3.1 Problem Description Figure 3.1 presents the schematic of a complete ZBO cryogenic liquid storage system including external cooling system and a cylindrical tank with spheroidal top and bottom. The tank wall is made of alumin um. A multilayered blanket of cryogenic insulation (MLI) has been att ached on the top of the aluminum shell. The tank is filled with liquid hydrogen. An inlet tube is attached to the top shell of the tank at one end and connected to a nozzle head submerged in the li quid at the other end su ch that the axis of symmetry or the centerline of the whole assembly is coincident with the centerline of the tank. The nozzle head has many nozzles as circ ular holes with their centers distributed on concentric circles on its front face. This st udy considers a nozzle head with three groups of nozzles: one single nozzle at the center a nd two polar arrays of nozzles whose centers are uniformly and densely distributed at full span and half span of the nozzle head. The annular outlet opening, also at the top of the tank, is concentric with the inlet opening and its outer radius is calculated such that their cross sectio nal areas are equal. Normally, even with the most efficient insulation struct ure applied, there is always heat leak from the surroundings into the fluid inside the tank. To prevent th e heat leak from eventually raising the liquid hydrogen to boiling point colder liquid hydrogen is pumped through the inlet tube to the nozzle head and injects into th e bulk fluid inside the tank through nozzle holes to displace the heated fluid th at exits the tank through the outlet opening on
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33 the top shell. The heated fluid then goes into the external cooling system, rejects the heat to cool down and returns to the inlet to complete a working cycle. Steadystate fluid flow and heat transfer phenomena for liquid hydrogen inside the tank were studied. The symmetry of the domain suggests the use of an axisymmetric model instead of a costly 3D model, provide d that the nozzles at full span and half span on the nozzle head are distributed densely enough to be approximated as annulus openings. Figure 3.2 shows the used axisymmetric model with essential dimensions of the tank and the inlet tubenozzle head assembly (the actual comput ational domain only occupies the right half of the sketch but the whole axial cross secti on of the tank is shown for clearer illustration purpose). The cylindrical body and the ellips oidal top and bottom of the tank wall are shown as solid curves including a stra ight line and elliptic arcs. In Figure 3.2, the inlet tubenozzle head assembly, whose axis is co incident with the centerline of the tank and also the zaxis, is shown as solid lines with gaps representing the thr ee groups of polar distributed nozzle openings. The essential dimensions of the storage ta nk are denoted in general form using the capital letters AD, FH, LN, P, and Q shown in Figure 3.2. This study only considers the effects of the diameter of the inlet tube D, the depth of the nozzle head from the top of the tank H, and the radius or the span of the nozzle head L. The fixed dimensions used for this study are given in Table 3.1. Table 3.1 Numerical values of fixed dimensions in Figure 3.2 Dimension A B C G M N P Value, m 1.50 0.65 1.30 0.05 0.01 0.02 0.02
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34 Cryocooler Heat exchanger Controller Solar array Nozzle head Tank wall Insulation Liquid cryogen Outlet Inlet Radiator Heat flux from surroundings Nozzle head plan view Figure 3.1 Schematic of cryogenic storag e system with inj ection nozzle head B C B M Q N P G L F A Outlet Tank wall Nozzle headInlet H D r z Figure 3.2 Axisymmetric model and essential dimensions
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35 The design parameters under investigation D, H, and L can take several different values corresponding to eleven simulation cases shown in Table 3.2. Table 3.2 Simulation cases for st orage tank with nozzle head Case # H, m L, m D, m H* L* D* Notes 1 1.3 1.0 0.15 0.87 0.67 0.10 Base H, L, D values 2 0.8 " 0.53 " Low H value #1 3 1.1 " 0.73 " Low H value #2 4 1.5 " 1.00 " High H value #1 5 1.8 " 1.20 " High H value #2 6 1.3 0.9 0.87 0.60 Low P value 7 1.1 " 0.73 High P value #1 8 1.2 " 0.80 High P value #2 9 1.3 " 0.87 High P value #3 10 1.0 0.10 0.67 0.07 Low D value 11 " 0.20 " 0.13 High D value The dimensions F and Q are calculated from the values of the other dimensions to satisfy the given requirements (for F, inlet and outlet areas are the same; and for Q, the nozzles in the second group has their centers at half span of the nozzle head) and can be calculated using the following formulas: 2 D F (3.1) 2 P N M L Q (3.2)
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36 The heat leak into the fluid is represented as a heat flux of qwall = 1 W/m uniformly distributed over the entire surf ace of the tank wall. Cooled supply fluid at Tcool = 18 K flows into the tank at a normal velocity of V = 0.01 m/s through the inlet opening. The relevant physical properties of liquid hydrog en are taken as constants at a reference temperature of 20 K as follows: = 71.1 kg/m, = 13.6 6 Pa.s, cp = 9.53 J.kg .K k = 0.0984 W.m .K 3.2 Computational Model 3.2.1 Governing Equations The Reynolds decompositions approach with a mixing length turbulence model is used for modeling the fluid flow and heat transfer. The governing equations representing the conservation of mass, momentum, and ener gy for steady state fl ow of liquid hydrogen in the tank as an incompressible fluid of constant properties in microgravity condition can be written for the axisymmetric model as: 0 1 z u ru r rz r (3.3) 2 21 z u ru r r r r p z u u r u ur r r z r r (3.4) 2 21 z u r u r r r z p z u u r u uz z z z z r (3.5) 2 21 z T r T r r r k z T u r T u cz r p (3.6) 3.2.2 Boundary Conditions The boundary conditions on velocity are On inlet opening: V u uz r 0 (3.7)
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37 On tank centerline: 0 0 r u uz r (3.8) On all solidfluid interfaces: 0 z ru u (3.9) The boundary conditions on temperature are On inlet opening: coolT T (3.10) On tank wall: wallq n T k (3.11) On tank centerline: 0 r T (3.12) 3.2.3 Numerical Solution For each simulation case in Table 3.2, a mesh of about 35000 quadrilateral elements was generated. Three layers of regul ar and refined elements of 4 mm height for the first layer and growth ratio of 1.25 are assigned along all fluidsolid interfaces where high rates of momentum and h eat transfer exist. The regi on inside the inlet tube and nozzle head is filled with st ructured 10 mmsize normal elements by using the map mesh option. The rest of the domain is filled with unstructured 12 mmsize normal elements using the pave mesh option. A typical mesh generated for the base case (simulation case 1) is shown in Figure 3.3. The FISOLV module of FI DAP was set up to solve the set of nonlinear algebraic equations resulted from the application of the Galerkin finiteelement procedure to the set of governing equa tions and boundary conditions, Equations (3.3) through (3.12), on the computational domain us ing the fully coupled successive substitution algorithm with a to lerance of 0.0001 for both the relative error and residual convergence criteria. The resul ting numerical solution gives tw o components of velocity, pressure, and temperature at every nodal poi nt over the entire computational domain.
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38 Figure 3.3 Quadrilateralelement mesh for axisymmetric model of storage tank with arrays of injection nozzles on nozzle head
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39 3.2.4 Dimensionless Parameters For better consideration in general context, th e geometric design parameters D, H, and L can be presented in dimensionless form as D*, H*, and L* (also given in Table 3.2) by scaling the original dimensions to A (the radius of the tank) as: A D D (3.13) A H H (3.14) A L L (3.15) As a constant speed V at the inlet opening is considered, the inlet diameter D can also be presented in dimensionless form by using the Reynolds number defined as: D ReV (3.16) The arc length coordinate is introduced fo r analyzing the local heat transfer on the tank wall. It is measured along the generatrix of the surface of revolution that forms the tank wall from the center of the bottom. The total length of the generatrix is calculated as S = 4.7 m. Similar to the geometric design para meters, the arc length coordinate is scaled to the characteristic length A as: A s s (3.17) The distributions of fluid speed and temp erature can be stud ied quantitatively by examining the average and standard deviation of speed as well as the maximum, average, and standard deviation of temperature. Flui d speed and temperature can be presented in dimensionless form as: V U U (3.18)
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40 A *wall coolq k T T T (3.19) The thermal performance of the heat pi pepumpnozzle system can be assessed by using a linear heat transfer model with the heat transfer coefficient defined as: cool wall wallT T q h (3.20) The heat transfer coefficient can be e xpressed in term of the dimensionless Nusselt number (Nu = hA/k) as: wall cool wall wall1 A Nu T T T k q (3.21) The average Nusselt number taken over the tank wall can be computed as: Sds s S0Nu 1 Nu (3.22) 3.3 Results and Discussion Figure 3.4 shows the distributions of flui d velocity and temperature for the base case (simulation case 1). In Figure 3.4a, the color of the filled background represents the magnitude of velocity or speed and the stream lines shows the directions of the fluid flow. In Figure 3.4b, the temperature distribution is shown by a filled plot with the color range representing the value of temperature. The co ld fluid enters the inlet opening at full speed 0.01 m/s, flows along the inlet tube as a typica l flow in circular pi pe, to the nozzle head, and then spreads radially inside the nozzle he ad before injecting into the bulk fluid. Temperature inside the inlet tube and the nozzl e head does not change much thus is quite uniform and is as low as the inlet temperatur e. Once the flow reaches the front face of the nozzle head, it splits into three groups of flow (labeled 1, 2, and 3 in Figure 3.4a)
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41 corresponding to three groups of nozzle ope nings on the nozzle head. The first group goes straight ahead through the center nozzle an d directly injects into the bulk fluid at a speed as high as that at the inlet opening, creates a disturbance in a local region along the centerline and gets retarded shortly by the massive stagnant bulk fluid at the bottom of the tank. This flow gives the bulk fluid a sm all region of low temperature localized along the centerline right outside the nozzle. As the re st of the fluid spread s in radial direction inside the nozzle head, the fl ow cross section area increa ses thus the fluid velocity decreases and the flow loses momentum. The fl ow tends to remain on its radial direction and travel the full span of the nozzle head rath er than to change direction to exit at half span. Therefore, the second group of flow corresponding to the second nozzle group is quite weak and only can create small disturba nces locally. The third nozzle group at full span of the nozzle head is wh ere the supply cold fluid inje cts into the bulk fluid more strongly and shows significant effects on coolin g. Also drawn by the pressure gradient toward the outlet opening, the flow exits the noz zle head at a directi on that bends toward the wall of the tank. It reaches the wall a nd then moves upward while sweeping along the wall toward the outlet opening at quite hi gh speed due to the influence of the low pressure there. Under the effect of this flow a strong circulation is formed in the region above the nozzle head (labeled as C1 in Figure 3.4a). This third circulation creates a well mixed thus low temperature region there. Since this flow cannot reach the top shell of the tank, a region of stagnant flui d exists there (labeled as S1 in Figure 3.4b). It can be observed in Figure 3.4b that this region has highe r temperature and that temperature decreases from the wall inward in isotherm al layers that shows the heat conduction pattern. As the third flow injects into the bulk fluid, it also aff ects the region under the
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42 nozzle head by combining with the second flow to form a circulation there (labeled as C2 in Figure 3.4a) resulting in anot her wellmixed region of low temperature but not as low as the one in the region above the nozzle head The fluid between this region and the low temperature region created by the first flow is barely moved and results in higher temperature (labeled as S2 in Figure 3.4b). The spot of ma ximum temperature can be resided in one of these two stagnant regions and right at the tank wall. The patterns of fluid flow and temperat ure distributions shown above suggests that if the nozzle head is placed deep down toward the bot tom of the tank, it may extend the well mixed region above the nozzle head as well as reduce the stagnant region under it thus improve the cooling performance of the system. Figure 3.5 shows the velocity field and temperature distribution for simulati on case 5, which has the largest value of the nozzle head depth H among the simulations. It can be observed that the patterns of both velocity and temperature distributions are si milar to those of the base case. The well mixedlow temperature region above the nozzle head extended as expected. The region under the nozzle head has a lowe r and more uniform temperature compared to that of the base case especially the stagnanthigher te mperature region at the bottom of the tank (labeled as S2 in Figure 3.5b). However, since the nozzle head is put that far away from the top, the fluid has to trav el a longer distance to reach th e top of the tank toward the outlet. Therefore, it cannot reach as closely to the top shell of the tank wall as in the base case to transport the heat away and reduce the temperature th ere. As a result, the region of stagnant fluid of high temp erature there (labeled as S1 in Figure 3.5b) expands much larger. That means there will be more chances for a higher maximum temperature spot to exist in that region.
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43 (a) Streamlines and speed, mm/s (b) Temperature, K C1 C2 1 2 3 S1S2 Figure 3.4 Distributions of velocity and temperature, simulation case 1 (base case) (a) Streamlines and speed, mm/s (b)Temperature, K C1 C2 1 2 3 S1 S2 Figure 3.5 Distributions of velocity and temperature, simulation case 5 (H* = 1.2)
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44Figure 3.6 presents the effects of the dept h of the nozzle head on the distributions of speed and temperature. The data are from simulation cases 1 that realize five values of H and fixed values for the other geometri c parameters. The depth of the nozzle head H is measured from the top of the tank to the front face of the nozzle head and presented in its dimensionless form H*. Figure 3.6a shows that as H* increases the dimensionless average speed shows no significant changes ar ound 0.01 but the dimensionless standard deviation increases linearly from 0.035 to 0. 050. This means that the depth of the nozzle head increases the nonuniformity of the sp eed field but shows no effect in average. In Figure 3.6b, as H* increases from 0. 53 to 1.20, the dimensionless maximum temperature decreases from 0.2 to it minimal va lue of 0.07 at H* = 1, then increases to 0.09 at H* = 1.20. The dimensionless standard deviation varies from 0.02 to 0.01 in a similar trend. The dimensionless average temperature gradually decreases from 0.02 to 0.01 as H* increases from 0.53 to 1.20. Thes e results confirm the previous observations that if the nozzle head is clos er to the bottom of the tank, the cooling effectiveness can be improved (lower average temperature) but th e antiboilingoff effectiveness can only be improved up to an optimum of H* = 1.0. Th e latter may suffer a loss (higher maximum temperature) if H* increases further (H* > 1). In actual dime nsions, this optimum is at about the middle of the height of the ta nk slightly shifted toward the bottom. Figure 3.7 presents the results from simulation cases 1 and 6 through 9 on the effects of the span (radius) of the nozzle head L represented by its dimensionless form L*. The increase of L is in fact the incr ease of nozzle openings area for the second and third groups of nozzles since the larger span, the larger the circles on which the centers of the nozzles distributed thus more nozzles for each group.
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45 0 0.01 0.02 0.03 0.04 0.05 0.06 0.50.60.70.80.911.11.2 Dimensionless depth of nozzle headDimensionless speed Average Std.Dev.(a) Speed 0 0.05 0.1 0.15 0.2 0.50.60.70.80.911.11.2 Dimensionless depth of nozzle headDimensionless temperature Maximum Average Std.Dev.(b) Temperature Figure 3.6 Effect of depth of nozzle head on distributions of speed and temperature
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46 0 0.01 0.02 0.03 0.04 0.05 0.550.60.650.70.750.80.850.9 Dimensionless span of nozzle headDimensionless speed Average Std.Dev.(a) Speed 0 0.02 0.04 0.06 0.08 0.1 0.550.60.650.70.750.80.850.9 Dimensionless span of nozzle headDimensionless temperature Maximum Average Std.Dev.(b) Temperature Figure 3.7 Effect of span of nozzle head on distributions of speed and temperature
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47 In Figure 3.7a, it can be observed that as L* increases from 0.60 to 0.87, the dimensionless average speed decreases linearly and very slightly from 0.013 to 0.010 while the dimensionless standard deviation rema ins at a value of 0.043. This suggests that the span of the nozzle head has no si gnificant effect on sp eed distribution. Figure 3.7b shows that all the parameters of temperature distribution increase as L* increases from 0.60 to 0.87, dimensionl ess maximum temperature from 0.08 to 0.09, dimensionless average temperature from 0. 01 to 0.02, and dimensionless standard deviation from 0.008 to 0.011. A value of L* can be selected around the base value L* = 0.67 where the maximum temperature take its lowest value (Figure 3.7b) or at least in the range 0.6.75, without significant loss on thermal effectiveness. Figure 3.8 presents the effects of Reynol ds number that represents the inlet diameter D on the distributions of speed a nd temperature from the results of simulation cases 1, 10 and 11 where D has three different values and the other geometric parameters remain at their base values. It can be observed in Figure 3.8a that both dimensionless average speed and standard deviation increase in a linear fashion as the Reynolds number increases from 5200 to 10400, in the range s 0.005.024 and 0.028.058, respectively. This suggests that increasing inlet diameter resu lts in higher fluid speed overall, which is well expected since the change of the inlet di ameter is directly pr oportional to the change of supply flow rate while the inlet velocity remains the same, and higher nonuniformity in the flow speed field. Figure 3.8b shows that the dimensionle ss maximum and average temperatures both decrease, respectively from 0.13 to 0. 07 and from 0.03 K to 0.01, as the Reynolds number increases from 5200 to 10400. However, as the Reynolds number increases, the
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48 slope of the temperature curve reduces signi ficantly, implying that the inlet diameter should be designed at a proper value such th at the positive effects it brings should overcompensate the energy used for pumping fluid at higher flow rate. This proper value for inlet diameter can be only determined by c onsidering the total energy consumption of the entire system including devices external to the tank such as the pump which is beyond the scope of the present study. For the same range of Reynolds number, the dimensionless standard deviation of temper ature also decreases from 0.02 to 0.005, which shows that mixing effectiveness (more uniform temperatur e distribution) can al so be improved with higher flow rate. Figure 3.9 shows the dimensionless wa ll temperature and Nusselt number with selected cases of geometry settings with ba se, low, and high values for each geometric parameter. The base case has H* = 0.87, P* = 0.67, and D* = 0.10 (H = 1.3 m, and P = 1.0 m, G = 0.15 m). The legends for other case s only show the parameter that is different from the base case. Since the highest temper ature should be located at the wall where the heat flux penetrates, the maximum wall temper ature is also the maximum temperature in the entire fluid body. In Figure 3.9a, it can be observed that fo r most cases there are two peaks or raising regions on the graph representing two stagnant regions of high temperature. The case of H* = 0.53 (low H) have only one outst anding peak at the bottom of the tank. This is the case where the nozzle head is very clos e to the top and therefore the stagnant region at the top is eliminated but the stagnant re gion at the bottom is expanded to a wide region with highest maximum temperature compared to that of other cases. The base case as well as most of the other cases has the notab ly higher first peak (stagnant region at the
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49 bottom) and the second peak (stagnant region at the top) leveled out except for the case H* = 1.2 (high H) where both peaks are shown and the peak at the t op is higher than the peak at the bottom. This means that the ma ximum temperature spot is resided in the stagnant region at the top for the case of high H and in the stagnant region at the bottom for the rest. As D* decreases, the maximum te mperature spot increases in magnitude as expected and moves far away from the center of the bottom. Lowest wall temperature is found for the case D* = 0.13 (high D). Figure 3.9b shows Nusselt numbers for the same set of cases of geometry settings as functions of dimensionless arc length coordinate. Since Nusselt number is inversely proportional to temperature difference, its profil e is similar to that of wall temperature being flipped over. Higher Nu sselt number means better th ermal performance the system has. For all cases, Nusselt number ranges from 5 to 75 with the maximum value (most effective heat transfer) belongs to the case of D* = 0.13. Figure 3.10 presents the average Nusse lt numbers as functions of geometry settings. The data were extracted from the same representative set of simulations described above. In general, the average Nu sselt number ranges from 14 to 39. Lower and higher D gives lower and higher Nusselt numb er, respectively. This means that as the inlet diameter increases thus flow rate incr eases, the average thermal performance of the system is improved. If the flow rate is ke pt unchanged, the averag e thermal performance can be improved by increasing the depth of th e nozzle head H. However, this approach should be used with caution since it may decrease antiboi lingoff effectiveness as discussed previously. The change of span of the nozzle head L shows only small effect on the average Nusselt number.
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50 0 0.01 0.02 0.03 0.04 0.05 0.06 500060007000800090001000011000 Reynolds numberDimensionless speed Average Std.Dev. 5 3 60 3 70 3 8 3 9 3 1 4 1.1 4 (a) Speed 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 500060007000800090001000011000 Reynolds numberDimensionless temperature Maximum Average Std.Dev. 5 3 610 3 7 3 810 3 9 3 14 1.1 4 (b) Temperature Figure 3.8 Effect of inlet diameter on distributions of speed and temperature
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51 0 0.05 0.1 0.15 0.2 0.25 00.511.522.533.5 Dimensionless arc length coordinateDimensionless wa ll temperature Base D* = 0.07 D* = 0.13 H* = 0.53 H* = 1.20 L* = 0.60 L* = 0.87(a) Wall temperature 0 10 20 30 40 50 60 70 80 00.511.522.533.5 Dimensionless arc length coordinateNusselt number Base D* = 0.07 D* = 0.13 H* = 0.53 H* = 1.20 L* = 0.60 L* = 0.87(b) Nusselt number Figure 3.9 Effect of geometry settings on wall temperature and local Nusselt number
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52 0 10 20 30 40(Base) D*=0.10 H*=0.87 L*=0.67 (Low D) D*=0.07 H*=0.87 L*=0.67 (High D) D*=0.13 H*=0.87 L*=0.67 (Low H) D*=0.10 H*=0.53 L*=0.67 (High H) D*=0.10 H*=1.20 L*=0.67 (Low L) D*=0.10 H*=0.87 L*=0.60 (High L) D*=0.10 H*=0.87 L*=0.87Geometry settingsAverage Nusselt number Figure 3.10 Average Nusselt number as function of geometry setting 3.4 Conclusions For this design of ZBO cryogenic storage tank for liquid hydrogen with arrays of injection nozzles distributed on a nozzle head, the supply cold fluid discharged through a nozzle penetrates into the bulk fluid inside the tank as a subm erged jet that mixes with the bulk fluid and cools it down as the jet lose s its momentum. The results show that higher temperature is encountered near the tank wall at two locations on the top and the bottom. The nozzle head is best located in the middl e part of the tank sin ce this provides better antiboilingoff effectiveness by lowering the maximum temperature of the fluid. Supply flow rate can be increased by means of increasing the inlet diameter while maintaining the same inlet speed which gives better th ermal performance with lower maximum and average temperatures. However, as the flow rate increases, higher energy consumption is
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53 required for running the pump a nd the cryocooler. This parameter needs to be designed in interaction with others to obt ain an optimum efficiency for the whole system. As the span of the nozzle head increases, the total area of the nozzle openings increases thus the speed of the jets injected into the bulk fluid through the no zzles reduce. This re sults in a slightly rise in both maximum and aver age temperatures. The best range for this parameter is 0.60.75 the radius of the tank. In designing a ZBO cryogeni c liquid storage system, th e maximum temperature is the key factor that needs attention. Location as well as dimensions of the active cooling subsystem (in this case, the inlet tube nozzl e head assembly) affect the performance of the storage tank at different level. There is no simple way to decide which dimension is significant or not. Simulations for parametric study need to be planned and performed to determine the effects of each parameter and their interactions. E xperimental design can be used for planning the parametric study.
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54 Chapter 4 Analysis of Heat Transfer in Cryogeni c Liquid Hydrogen Tank with Heat Pipe and Array of PumpNozzle Units 4.1 Problem Description This chapter presents a steadystate analysis for fluid flow and heat transfer in a ZBO cryogenic storage tank for liquid hydrogen equipped with a heat pipe and a polar array of pumpnozzle units. The schematic of the storage system is shown in Figure 4.1. The storage tank has a cylindric al body with oblate spheroidal top and bottom. The tank wall is made of aluminum covered by a multilayered blanket of cryogenic insulation. The tank is connected to a cryocooler via a heat pipe to dissipate the heat leak through the insulation and the tank wa ll into the fluid within the tank. The condenser section of the heat pipe dissipates heat to the cryocooler while the evaporat or section of the heat pipe picks up heat from the fluid. H eated fluid is directed onto the evaporator section at the tip of the heat pipe by a polar array of many pu mpnozzle units circumfe rentially distributed around as shown in Figure 4.2a. Only the liquid hydrogen within the tank is modeled for computation. The surface of th e evaporator section is kept at a constant low temperature while the surface of the condens er section is thermally insulated. The symmetry of the domain suggests the use of an axisymmetric mo del rather than a full 3D one in order to reduce computing resources required while it still produces adequate results. Figure 4.2b shows the axisymmetric model with the axis of symmetry or the centerline of the tank coincides with the z axis along which the heat pipe located.
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55 Cryocooler Heat exchanger Controller Solar array Pumpnozzle units Tank wall Insulation Heat pipe Liquid cryogen Radiator Condenser Evaporator Heat flux from surroundings Figure 4.1 Schematic of cryogenic storage system with polar array of pumpnozzle units (a) Threedimensional arrangement (b) Axisymmetric model and dimensions Figure 4.2 Threedimensional domain and simplified axisymmetric model
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56 The essential geometric dimensions are deno ted in general form as capital letters. The fixed dimensions used in this study are given in Table 4.1. Table 4.1 Numerical values of fixed dimensions in Figure 4.2b Dimension A B C D E F L M N R Value, m 1.50 0.65 1.30 0.20 0.30 0.20 0.30 0.10 0.10 0.10 Seven geometry settings are considered to investigate th e effects of several design parameters including G (the spraying gap be tween the nozzle surface and the heat pipe), H (the length of the heat pipe), and P (the length of the inlet tube). Each parameter has a set of assigned values: base, low and high. The base geometry setting is composed by using the base values for all three geometric parameters. Six other geometry settings are built by taking the base setting then changing on ly one geometric parameter to its low or high value from its base value. For each geometry setting, five values of prescribed fluid speed at nozzle are considered. Details on the simulation cases are given in Table 4.2. Table 4.2 Simulation cases for storage tank with heat pipe and array of pumpnozzle units Case # G, m H, mP, m Speed at nozzle V m/s Notes 1 0.2 1.5 0.55 0.01, 0.02, 0.03, 0.04, 0.05 Base G, H, P values 6 0.1 " Low G value 11 0.3 " High G value 16 0.2 1.0 " Low H value 21 2.0 " High H value 26 1.5 0.25 Low P value 31 " 0.85 High P value
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57 The heat leak into the fluid is represented as a heat flux of qwall = 1 W/m uniformly distributed over the entire surf ace of the tank wall. The temperature on the surface of the evaporator sect ion of the heat pipe is Tcool = 20 K. The values for the normal speed at the nozzle face V are given in Table 4.2. The numerical values of the fluid properties were taken as constants at a reference temperature of 20.3 K as follows: = 70.8 kg/m, = 13.26 Pa.s, cp = 9.66 J.kg .K k = 0.0989 W.m .K 4.2 Computational Model 4.2.1 Governing Equations The Reynolds decompositions approach with a mixing length turbulence model is used for modeling the fluid flow and heat transfer. The governing equations representing the conservation of mass, momentum, and ener gy for steady state fl ow of liquid hydrogen in the tank as an incompressible fluid of constant properties in microgravity condition can be written for the axisymmetric model as: 0 1 z u ru r rz r (4.1) 2 21 z u ru r r r r p z u u r u ur r r z r r (4.2) 2 21 z u r u r r r z p z u u r u uz z z z z r (4.3) 2 21 z T r T r r r k z T u r T u cz r p (4.4) 4.2.2 Boundary Conditions To completely define the problem, appr opriate boundary conditions are required on the boundary of the computational domai n. The boundary conditions on velocity are
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58 On nozzle face: 0 z ru V u (4.5) On centerline: 0 0 r u uz r (4.6) On all solidfluid interfaces: 0 z ru u (4.7) The boundary conditions on temperature are On tank wall: wallq n T k (4.8) On evaporator section: coolT T (4.9) On other boundary surface: 0 n T (4.10) 4.2.3 Numerical Solution The FIGEN module of FIDAP was used for the geometric modeling and mesh generation for the computational domain. A quadrilateralelement mesh of about 18000 elements as shown in Figure 4.3 was generated for each geometry configuration (Table 4.2) to achieve an acceptable accuracy with reasonable computing resources consumed. Larger size elements were used to fill most part of the domain while regular and properly refined element layers was assi gned around inlet, outle t, and solid surfaces to capture the high rates of change of momentum a nd heat transfer existing there. The FISOLV module of FIDAP was set up to solve the set of nonlinear algebraic equations resulted from the application of the Galerkin finiteelement procedure to the set of governing equations and bounda ry conditions, Equations (4.1) through (4.10), on the computational domain using the fully coupled successive substitution algorithm with a tolerance of 0.000001 for both the relative error and re sidual convergence criteria.
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59 Figure 4.3 Quadrilateralelement mesh for axisymmetric model of storage tank with heat pipe and polar array of pumpnozzle units
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60 4.2.4 Dimensionless Parameters For better consideration in general context, it is more efficient to present the relevant parameters and results in dimensi onless form. The forced flow speed at nozzle can be represented by the Reynolds nu mber at nozzle surface defined as: hVd Re (4.11) where the chosen characteristic di mension is the hydraulic diameter dh of nozzle outlet opening, which is modeled in the axis ymmetric model as a cylinder surface with radius of (G+D/2) and height of F (Figure 4.2b). The hydraulic di ameter is defined as "four times flow area divided by wetted peri meter" in textbooks such as White (1991) and can be found as: F 2 hd (4.12) The geometric parameters are presented in dimensionless form as: d G G (4.13) d H H (4.14) d P P (4.15) where the characteristic dimension d of th e tank is chosen as the radial distance from the surface of the evaporator section of the heat pipe to the tank wall and can be found as: 2 D A d (4.16) The arc length coordinate is introduced fo r analyzing the local heat transfer on the tank wall. It is measured along the generatrix of the surface of revolution that forms the tank wall from the center of the bottom. The tota l length of the generatr ix is calculated as
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61 S = 4.7 m. Similar to the geometric design para meters, the arc length coordinate is scaled to the characteristic length A (rather than the generatrix length S which may seem to be a more natural choice, to keep it consistent with the other parameters) as: d s s (4.17) Fluid speed and temperature can be pr esented in dimensionless form as: V U U (4.18) d q k T T Twall cool* (4.19) Using the numerical values used in this study, Equation (3.12) gives dh = 0.4 m and Equation (3.16) gives d = 1.4 m. Thus for the range of speed at nozzle given in Table 1, Equation (3.11) gives Re = 2.154 1.085. From Table 4.2 and Equations (3.13) through (3.15), the dimensionles s geometric parameters can ha ve the respective values as follows: G* = 0.07, 0.14, and 0.21, H* = 0.7, 1.1, and 1.4; P* = 0.2, 0.4, and 0.6. The base geometry setting (simula tion cases 1) has G* = 0.14, H* = 1.1, and P* = 0.4. For characterizing convective heat transfer, a h eat transfer coefficient is defined as: cool wall wallT T q h (4.20) From Equations (19) and (20), Nusselt number can be written as: wall cool wall wall1 A Nu T T T k q (4.21) The average Nusselt number can be found as: Sds s S Nu 1 Nu (4.22)
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62 4.3 Results and Discussion Figure 4.4 presents the distribution of velo city, pressure, turbulent viscosity, and temperature in the fluid for the base case with speed at nozzle V = 0.01 m/s (simulation 1). In Figure 4.4a, the filled background color re presents the magnitude (speed) and the streamlines represent the direction of velocity that show a complete view of the velocity field. Figure 4.4b shows the pressure distribution in the fluid flow also for simulation case 1. The fluid flow patter n can be observed on these two plots. The pump creates a pressure difference that drives the heated fl uid inside the tank toward the opening of the inlet tube of the pump. After being discharged from the nozzle, the flow spreads into two streams spraying on the evaporator section of the heat pipe. One stream goes up along the surface of the heat pipe brushing through the ev aporator section then the adiabatic section of the heat pipe, until it reaches the top of the tank, sweeps along the surface of the top shell of the tank before being collected at the inlet opening, making the first loop. The other stream moves down along th e surface of the evaporator section of the heat pipe, then the centerline, until it r eaches the bottom of the tank, sweeps along the wall of the tank over a longer distance before going to the inlet opening again, making the second loop. For both streams, the speed increases to maximum value as the streams sweeping along the heat pipe and the cente rline. The region of fluid inside these two loops, even though not directly driven by the pump, move under the influence of the loops and create two families of circulations that cover the upper part and the lower part of the tank. A small region exists at the wall between these two parts where no flow sweeps through thus remains still.
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63 (a) Streamlines and speed, m/s (b) Pressure, Pa (c) Temperature, K Figure 4.4 Distribution of velocity, pressure, and temperature, simulation case 1
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64 The temperature distribution in the fluid is shown in Figure 4.4c. Temperature distributes quite uniforml y over the entire domain. Figure 4.4c presents the temperature distribution over a small range of values to re veal its pattern. It can be observed that a lower temperature exists only in a narrow regi on right next to the h eat pipe and along the centerline. The rest of the domain is at a relatively higher temperature. The temperature pattern shows that convective heat transfer generally dominates the entire fluid domain. The highest temperature concentr ates along the tank wall, especi ally in the re gion of still fluid between the two families of circulations as mentioned above. There is also a small hot spot where the heat pipe is attached to the tank wall. These high temperature regions coincide with the regions of still flui d where the forced flow cannot reach. Figure 4.5 shows the change of distributi on of fluid speed in side the tank for different values of speed at nozzle and th e spraying gap G between the nozzle and the heat pipe. As Reynolds numb er increases from 2.154 to 1.085 (speed at nozzle increases from 0.01 to 0.05 m/s), dimensionl ess average speed and respective standard deviation remain constants. This shows th at both true average speed and standard deviation increase linearly. As the gap G betw een the nozzle and the heat pipe increases, the average speed and the standard deviation increases also. This trend can be readily expected since the increase of the gap result s in the increase of the area of the nozzle surface (modeled as a cylinde r surface of radius G + D/2 and height F, see Figure 4.2b for dimensions), hence the increase of pumping flow rate at the same speed at nozzle. To assess thermal performance of a system the three parameters, maximum temperature, average temperature, and standard deviation of temperat ure distribution, are considered. Maximum temperature represents an tiboiling effectiveness of the system in
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65 the sense that a lower maximum temperature gives a larger margin to the boiling point and thus can prevent boiling off better. Average temperature represents cooling effectiveness on the entire bulk fluid as a whole. Lower the average temperature characterizes better cooling system. The standa rd deviation of temperature represents the mixing effectiveness of the system. Lower st andard deviation means higher uniformity in the bulk fluid and less chance for a spot of higher temperature to exist where boiling off could have occurred. Figure 4.6 shows the effects of Reynolds number (representing speed at nozzle V) and the spraying gap G between the nozzle face and the heat pipe (represented by G*) on thermal performance of the system. As Re ynolds number increases, the three thermal performance parameters monotonically decreas e in a nonlinear manner with decreasing rates of change. This confirms that the in crease of Reynolds number will improve thermal performance of the system. It can be observed in Figure 4.6 that for each case of G, the curves of dimensionless maximum and average temperatures appear in pair of similar forms with an offset of about 0.02. The curves of dimens ionless standard devia tion for three cases of G appear in a group and refer to the second axis on the right of the graph that shows the values of these standard deviations are less than 0.1. As G increas es, thus pumping flow rate increases as mentioned previously, a ll three parameters increases and show a worsening of thermal performance. This obs ervation suggests that higher pumping flow rate will not necessarily ensure a better th ermal performance but higher speed at nozzle V (increasing pumping flow ra te) and lower spraying gap between the nozzle surface and the heat pipe G (decreasing pumping flow rate) will do.
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66 0.15 0.2 0.25 0.3 2E44E46E48E41E5 Reynolds numberDimensionless speed Average, G*=0.07 Average, G*=0.14 Average, G*=0.21 Std.Dev., G*=0.07 Std.Dev., G*=0.14 Std.Dev., G*=0.21 24 4104 6104 8104 105 Figure 4.5 Effect of speed at nozzle and spraying gap on speed distribution 0 0.05 0.1 0.15 0.2 0.25 2E044E046E048E041E051E05 Reynolds numberDimensionless temperature0 0.1 0.2 0.3 0.4 0.5Dimensionless std. deviation Maximum, G*=0.07 Maximum, G*=0.14 Maximum, G*=0.21 Average, G*=0.07 Average, G*=0.14 Average, G*=0.21 Std.Dev., G*=0.07 Std.Dev., G*=0.14 Std.Dev., G*=0.21 24 4104 6104 84 15 1.25 Figure 4.6 Effect of speed at nozzle and spraying gap on temperature distribution
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67 On analyzing the velocity distribution for the case of G* = 0.07 (G = 0.1 m, simulation case 6), it is found th at the pattern is similar to th at for the base case with G* = 0.14 (G = 0.2 m, simulation case 1). However, the maximum speed of the case G* = 0.07 is about 1.5 times higher than that of the base case with G* = 0.14 while the average speed of the former is still less than that of the latter as shown in Figure 4.5 and discussed above. In other words, the decrease of the spraying gap G leads to the decrease of total flow rate delivering to the heat pipe, thus the average speed, but also increases fluid speed in a local region located over the surface the heat pipe. This locally strengthened flow is significant for the enhancement of c onvective heat transfer over the surface of the evaporator section. This e xplains the previous observati on that smaller spraying gap G results in better thermal performance of the system. Figure 4.7 present the effects of the lengt h of the heat pipe H on average speed and maximum temperature for five different cases of Reynolds number (speed at nozzle V). The data were extracted from simu lation cases 1 and 16 where G and P were assigned their base values (see Table 4.2). In Figure 4.7a, it can be observed that fo r all cases of Reynolds number, the dimensionless average speed show the same patte rn, in a very small variation of less than 0.005, as H* increases that the highest av erage speed can be found corresponding to the base value (1.1) of H* Figure 4.7b shows the effects of H* on ma ximum temperature. It can be observed that H* has almost no effect for higher Reynol ds number but slightly stronger effect for lower Reynolds number where maximum temperat ure decreases as H* increases from 0.7 to 1.4.
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68 0.23 0.24 0.25 0.26 0.27 0.28 0.60.811.21.41.6 Dimensionless length of heat pipeDimensionless average speed Re=2.15E4 Re=4.30E4 Re=6.45E4 Re=8.60E4 Re=1.08E5(a) Average speed 0.05 0.1 0.15 0.2 0.25 0.60.811.21.41.6 Dimensionless length of heat pipeDimensionless maxi mum temperature Re=2.15E4 Re=4.30E4 Re=6.45E4 Re=8.60E4 Re=1.08E5(b) Maximum temperature Figure 4.7 Effect of length of heat pipe on average speed and maximum temperature
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69Figure 4.8 shows the effects of the length of the inlet tube P of the pumpnozzle unit (represented by its dimensionless form P*) on average speed and maximum temperature for five different cases of Reynolds number (re presenting speed at nozzle V). The data were extracted from the simu lation cases 1 and 26 where G and H were assigned their base values (Table 4.2). In Figure 4.8a, as P* increases, the dimensionless average speed decreases and shows the same pattern for all cases of Re ynolds number in less than 0.01 variation. Figure 4.8b shows that the dimensionless maxi mum temperature decrease slightly as P* increases from 0.2 to 0.6 for all Reynolds number. Instead of directly analyzing representa tive temperature parameters (maximum and average values and standard deviation) as shown previously, thermal performance of the system can be assessed by using a heat tran sfer model where the fluid is considered as a medium that the heat flux going in through th e tank wall is transported to the surface of the evaporator section of the heat pipe by m eans of diffusive and c onvective heat transfer. Figure 4.9 presents the wall temperature and Nusselt number as functions of the arc length coordinate. In Figure 4.9a, it can be observed th at all the curv es corresponding to five different Reynolds numbers (representi ng five speeds at nozzle V) have the same pattern. Dimensionless wall temperature distri butes quite uniformly on most parts of the tank except for the hot region in the middle of the cylindrical shell of the tank wall and the small hot spot at the end of the arc length where the heat pipe is attached to the tank wall. Overall dimensionless variation is less than 0.01. As Reynolds number (speed at nozzle) increases, wall temperature decreases.
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70 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.10.20.30.40.50.60.7 Dimensionless length of inlet tubeDimensionless average speed Re=2.15E4 Re=4.30E4 Re=6.45E4 Re=8.60E4 Re=1.08E5(a) Average speed 0 0.05 0.1 0.15 0.2 0.25 0.10.20.30.40.50.60.7 Dimensionless leng th of inlet tubeDimensionless maximum temperature Re=2.15E4 Re=4.30E4 Re=6.45E4 Re=8.60E4 Re=1.08E5(b) Maximum temperature Figure 4.8 Effect of length of inlet tube on average speed and maximum temperature
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71Figure 4.9b presents Nusselt numbers for th e base configuration (G = 0.2 m, H = 1.5 m, P = 0.55 m) corresponding to five cases of speed at nozzle V (simulation cases 1 5), represented as Reynolds number, as functi ons of dimensionless ar c length coordinate. Since Nusselt number is inversely proportional to temperature difference, its profile is similar to that of wall temperature being fli pped over. It can be observed that the lower the speed at nozzle, the more uniform Nu sselt number is. Higher Nusselt number means better thermal performance the system has. As speed at nozzle increases from 0.01 to 0.05 m/s (Re = 2.154 1.085), Nusselt number increases from 5 to 20. Figure 4.10 shows the dimensionless wall temperature and Nusselt number for Re = 2.154 ( V = 0.01 m/s) with all cases of geometry settings. The base case has G* = 0.14, H* = 1.1, and P* = 0.4 (G = 0.2 m, H = 1.5 m, and P = 0.55 m). The legends for other cases only show the parameter that is different from the base case. In Figure 4.10a, it can be observed that the si ngularity of peak temperature at the location where the heat pipe attached to the tank exists in all cases; most cases has the narrow hot region in the middle of the side of the tank wall except for the two cases, H* = 0.7 (H = 1.0 m, low H value) and P* = 0. 6 (P = 0.85 m, high P value), where the hot region extends toward the top of the tank; lowest wall temperature is found for the case G* = 0.07 (G = 0.1 m, low G value). Figure 4.10b shows Nusselt numbers for Re = 2.154 ( V = 0.01 m/s) and all cases of geometry settings as functions of dimensionless arc length coordinate. For all cases, Nusselt number ranges from 4.5 to 7.5 with the maximum value (most effective heat transfer) belongs to th e case G* = 0.07 (G = 0.1 m).
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72 0.04 0.08 0.12 0.16 0.2 00.511.522.533.5 Dimensionless arc length coordinateDimensionless wall temperature Re=2.15E4 Re=4.30E4 Re=6.45E4 Re=8.60E4 Re=1.08E5(a) Wall temperature 4 8 12 16 20 00.511.522.533.5 Dimensionless arc length coordinateNusselt number Re=2.15E4 Re=4.30E4 Re=6.45E4 Re=8.60E4 Re=1.08E5(b) Nusselt number Figure 4.9 Wall temperature and Nusselt number, base geometry setting
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73 0.12 0.14 0.16 0.18 0.2 0.22 01234 Dimensionless arc length coordinateDimensionless wall temperature Base G*=0.07 G*=0.21 H*=0.7 H*=1.4 P*=0.2 P*=0.6(a) Wall temperature 4 5 6 7 8 01234 Dimensionless arc length coordinateNusselt number Base G*=0.07 G*=0.21 H*=0.7 H*=1.4 P*=0.2 P*=0.6(b) Nusselt number Figure 4.10 Wall temperature and Nusselt number, Re = 21500
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74Figure 4.11 presents the average Nusse lt numbers for all cases of geometry settings as functions of Reynolds number (re presenting speed at noz zle). The data were extracted from all simulations performed in this study. In general, the average Nusselt number ranges from 4.7 to 28.8. For each cas e of geometry settings, the average Nusselt number increases almost linearly as the Re ynolds number increases. The graph of the case G = 0.07 (G = 0.1 m) stands alone and show far higher Nusselt number than that of the rest for any Reynolds number. The graphs of the other cases form a group where one does not show much difference from each othe r. This suggests that the low spraying gap has a much more significant effect on the average Nusselt number than other geometry parameters. 4 8 12 16 20 24 28 2E+44E+46E+48E+41E+5 Reynolds numberAverage Nusselt number Base G*=0.07 G*=0.21 H*=0.7 H*=1.4 P*=0.2 P*=0.6 24 4104 6104 8104 1105 Figure 4.11 Average Nusselt number as function of Reynolds number
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75 4.4 Conclusions The numerical simulations give better unde rstanding of the fluid flow and heat transfer phenomena needed for the design of a cryogenic storage ta nk for liquid hydrogen with heat pipe and array of pumpnozzle un its. Thermal performance of the system can be quantified by temperature parameters that represent antiboiling, cooling, and mixing effectiveness or by Nusselt numbe r that results from a heat transfer model. Higher speed at nozzle created by the array of pumpnozzle units results in better thermal performance of the system. Among various geometry para meters, the gap between the nozzle and the heat pipe (the spraying gap) plays a very important role in controlling the thermal performance of the system. Other parameters su ch as the length of the heat pipe and the length of the inlet tube have only slight effects. Significantly improved thermal performa nce for a design can be achieved by reducing the spraying gap or by increasing sp eed at nozzle. On design point of view, increasing speed at nozzle means higher power consumption on the array of pumpnozzle units and thus should be avoided if possible. The forced flow speed at the nozzle can be chosen to satisfy required thermal performa nce based on the heat load (the heat flux leaking through the tank wall insulation from the surrounding s). A model with designed geometry can be then set up and corresponding simulation can be run to verify the thermal performance of the design. It is s hown that numerical mode ling and simulation is a powerful tool for the process of desi gning and optimizing ZBO cryogenic storage systems.
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76 Chapter 5 ThreeDimensional Analysis of Heat Transfer in Cryogenic Liquid Hydrogen Tank with Heat Pipe and Lateral PumpNozzle Unit 5.1 Problem Description The overall schematic of the ZBO cryoge nic system for liquid hydrogen is shown in Figure 5.1. The tank wall is made of aluminum attached to a multilayered blanket of cryogenic insulation on its top. The tank is conne cted to a cryocooler via a heat pipe to dissipate the heat leak through the insulation and tank wall into the fluid within the tank. The condenser section of the heat pipe di ssipates heat to the cryocooler while the evaporator section of the heat pipe picks up heat from the fluid within the tank. The hot fluid is directed to the eva porator section of the heat pi pe by using a fl uid circulatory system within the tank. This system consists of a pump, a nozzle head for discharge of fluid and a suction tube feedi ng to the pump. Only the fluid inside the tank is modeled. Several different discharge sp eeds were investigated to fi nd an optimum operating setting for the ZBO hydrogen storage system. Steadystate distributions of velocity and temperature were computed. This chapter presents a parametric analysis for the fluid flow and heat transfer, focusing on the effect of the normal speed discharged at the nozzle face. Although it costs more computing resour ces, a threedimensional (3D) model as shown in Figure 5.2 is employed since the axisymme tric one is now no longer the case. In addition, axisymmetric simulations (see Chapter 4 for details) with the same parameters as their 3D counterpart s were also computed for relative comparison.
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77 Cryocooler Heat exchanger Controller Solar array Pumpnozzle unit Tank wall Insulation Heat pipe Liquid cryogen Radiator Condenser Evaporator Heat flux from surroundings Figure 5.1 Schematic of cryogenic storage system with single lateral pumpnozzle unit E H F L M N y B C B R A zx P D G (a) Threedimensional domain (b) Essential dimensions Figure 5.2 Computational model and dimensions
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78 In Figure 5.2b, the essential geometric dimens ions are denoted in general form as capital letters. The values of the dimens ions used in this study are given in Table 5.1. Table 5.1 Numerical values of fixed dimensions in Figure 5.2b Dimension A B C D E F G H L M N P R Value, m 1.50 0.65 1.300.200.300.200.201.500.300.10 0.10 0.800.10 The heat leak into the fluid from the su rroundings is considered as a heat flux of qwall = 2 W/m uniformly distributed over the entire surface of the tank wall. The heat generated by the running pump is modeled at a heat flux of qpump = 0.01 W/m uniformly distributed over the wall of the pump body. The temperature on the surface of the evaporator section of the heat pipe is Tcool = 18 K. The values for the normal speed at the nozzle face V are given in Table 5.2. The numerical values of the fluid properties were taken as constants at a reference temperature of 20.3 K as follows: = 70.8 kg/m, = 13.26 Pa.s, cp = 9.66 J.kg .K k = 0.0989 W.m .K Table 5.2 Simulation cases for storage tank with heat pipe and lateral pumpnozzle unit Model 3D Axisymmetric Case # 1 2 3 4 5 6 7 8 9 10 Fluid speed at nozzle V m/s0.010.020.030.040.050.010.02 0.03 0.040.05 5.2 Computational Model 5.2.1 Governing Equations The Reynolds decompositions approach with a mixing length turbulence model is used for modeling the fluid flow and heat tr ansfer. Steady state, incompressible flow of
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79 liquid hydrogen is considered. The equation for the conservation of mass, momentum, and energy can be written for the 3D model in rectangular coordinates as: 0 z u y u x uz y x (5.1) 2 2 2 2 2 2z u y u x u x p z u u y u u x u ux x x x z x y x x (5.2) 2 2 2 2 2 2z u y u x u y p z u u y u u x u uy y y y z y y y x (5.3) 2 2 2 2 2 2z u y u x u z p z u u y u u x u uz z z z z z y z x (5.4) 2 2 2 2 2 2 pz T y T x T k z T u y T u x T u cz y x (5.5) 5.2.2 Boundary Conditions The boundary conditions on veloci ty and on temperature are On nozzle face: 0 z y xu u V u (5.6) On plane of symmetry: 0 0 y u y u uz x y (5.7) On fluidsolid interfaces: 0 z y xu u u (5.8) On evaporator section: coolT T (5.9) On tank wall: wallq n T k (5.10) On pump wall: pumpq n T k (5.11) On other boundary surfaces: 0 n T (5.12)
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80 5.2.3 Numerical Solution For solving the governing equations numeri cally by using finite element method, the computational domain needs to be discretized into small elements. For a 3D domain of irregular shape as this is, it is easier to generate a mesh of tetrahedral elements (most meshing program has the option to generate the mesh automatically) but the number of elements will be very large, yielding to more computing resources required sometimes may exceed available resources or become im practical. The hexahedralelement mesh for a complex geometry, on the other hand, usually ta kes longer to generate due to the lack of an existing fully automatic meshing option, but can reduce the number of elements, thus can reduce computing resources required, signi ficantly. For this study, the geometry and mesh generation software GAMBIT (Fluent, 200 6) was used with a systematic meshing strategy to generate a fully hexahedral mesh for the 3D model. The irregular geometries are encapsulated in box shapes, leaving the main space as a combination of box shapes that can be meshed automatically with cuboi d elements. The encapsulated geometries are meshed separately to accommodate the irregul ar geometries while maintaining the mesh on the outer of the zone match that of th e main space. The final mesh of about 39000 hexahedral elements as shown in Figure 5.3 to achieve acceptable accuracy with reasonable computing resources employed. Figure 5.3c shows the expanded view focusing on the region around the heat pipe tip and the pumpnozzl e unit where highly irregular geometry is located. Larger size regula r elements were used to fill most part of the domain while properly refined element la yers was assigned around inlet, outlet, and solid surfaces to capture the high rates of ch ange of momentum and heat transfer that exist there.
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81 (a) Full view (b) Heat pipe and pumpnozzle unit (c) Expanded view of pumpnozzle unit and evaporator section of heat pipe Figure 5.3 Hexahedralelement mesh for 3D model of storage tank with heat pipe and lateral pumpnozzle unit
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82 Since fully coupled algorithms are not prac tically applicable du e to large number of elements in a 3D computa tional domain of highly irregul ar geometry, the segregated algorithm was used to solve th is system of finite element equations. The convergence criterion of relative errors was us ed with the tolerance set at 0.0001. 5.3 Results and Discussion Figure 5.4 shows the velocity field of th e flow of liquid hydrogen inside the tank for the base case (simulation case 1). For reve aling the complex struct ure of the 3D fluid flow, three subplots are employed for streamlines speed distribution, and velocity vectorspeed distribution combined. Figure 5.4a presents nine colorcoded streamlines that starts from a three by three regular spaced positio ns on the nozzle face and represents the typical flow pattern. The pump creates a pre ssure difference that draws the fluid inside the tank towards the inlet of the suction tube The fluid enters the suction tube of the pump and moves towards the nozzle. In the noz zle, the flow expands, thus reduces speed, and then exits through many tiny holes on the nozzle face. After being discharged from the nozzle, the fluid flow spreads into many streams wrapping around the evaporator section of the heat pipe, which is maintained at a low constant te mperature of 18 K. We can roughly classify three groups of streams moving in three main directions. The first group sweeps along the cylindrical part of the evaporator sect ion of the heat pipe, then the heat pipe adiabatic section, until it re aches the top, sweeps along a short portion on the top before being collected again at th e suction tube inlet. The second group moves down along the tip of the heat pipe, wraps around the spherical part of the heat pipe then moves towards the bottom and creates a strong ci rculation in the regi on on the left below the heat pipe. The third group of streams is th e main part which wraps around the side of
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83 the cylindrical part of the heat pipe toward s the open space on the left side of the heat pipe. In the absence of any obstacle, this group of streams reaches the wall of the tank and sweeps through most of the middle and upper part of the tank wall before returning to the pump side and being collected at the suction tube inlet. Figure 5.4b presents the flow speed isosurfaces (surface that represents poi nts of a constant value of speed) with the color representing the speed level. At the nozzle face, the fluid speed is 0.01 m/s as assigned by its boundary condition. At the inlet of the suctio n tube, the fluid speed is about 0.04.05 m/s which is consistent with the estimated average speed of 0.04 m/s there, based on crosssectional area ratio a nd continuity condition. The fluid speed around the evaporator section of the heat pipe is about 50% of the di scharge speed at the nozzle face. Figure 5.4c presents a closeup view of velocity field in the region surrounding the nozzle and the evaporator sectio n of the heat pipe. The arrows represent the velocity vectors on a colorcoded background that represents speed distribution. Only quarters of the fluid volume and the heat pipe are viewed to show the velocity field on both the direct impinged zone and the side of the heat pipe. It shows more clearly the speed distribution and how the flow wrapping around the heat pipe there. Figure 5.5 shows the temperature distribu tion inside the tank for the base case (simulation case 1). For the problem at hand in which the fluid is heated up by heat flux applied on the tank wall, temperature on the wall is always higher than that of the fluid inside. The pattern of temperature on the tank wall and how it changes inward the bulk fluid is of interest. For revealing the co mplex structure of th e 3D distribution of temperature, four subplots are employed. Figure 5.5a presents a sl ice plot with the slice surface that conforms to and 5 cm from the tank wall. The first group of streams does not
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84 show much a significant effect except for a small spot of hi gh temperature right above the inlet of the suction tube which can be explained as follows: as the fluid is being collected at the inlet of the suction tube, the flows would sweep through the wall nearby but since they bend towards the inlet, there is no fl ow sweeping through th at area and it behaves like a stagnant region. The second group of stre ams moves down to the left cools down a part of the bottom but the circulation is c onfined in a small region preventing the cool fluid to spread further to the right, leaving the part of the tank wall on the right of the heat pipe at higher temperature. A part of the flui d close to the tank wall on the left side (the opposite side to the pumpnozzle unit) is kept at a lower temperatur e since the third group of fluid streams splash and spread on it with an incoming flow cooled on the evaporator section of the heat pipe. This part extends up to half of the tank wall on the left side. As the second and third groups of streams leave the lower part on the right side almost undisturbed, this region shows the pattern of diffusive heat transfer, confirming the absence of any strong fluid stream and thus c onvective heat transfer in this region; an area of high temperature exis ts there as the result. Figure 5.5b presents the isosurfaces fo r temperature showing how the high temperature regions extend into the bulk flui d. The innermost isosurface is for 18.1 K has several peaks that locate the higher temperature regions bene ath them. Beside the two hot areas observed in Figure 5.5a, there is another one at the middle side of the tank. Parts (c) and (d) of Figure 5.5 present the views from front and back of the slice plot with slice surfaces are planes perpendicu lar to the axis of the tank. They show how the hot regions extend into the bulk fluid. Th e hot region on the botto m of the tank is the most extended one, both spreading on the wall and into the bulk fluid.
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85 (a) Streamlines (b) Speed, m/s (c) Velocity vector and speed, m/s Figure 5.4 Velocity distribution, m/s, simulation case 1
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86 (a) Conformal slice plot (b) Isosurfaces (c) Axial planar slice plot, front (d) Axial planar slice plot, back Figure 5.5 Temperature distribution, K, simulation case 1
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87Figure 5.6 presents a comparison of the temperature distribution pattern on the symmetry plane for simulation case 1, Figure 5.6a, as the typical case for 3D simulations, and simulation case 6, Figure 5.6b, as the typical case for axisymmetric simulations. Figure 5.6b was created by putting together a temperature distribution plot of simulation case 6 with its mirror image. Bounda ry conditions and dimensions are also the same for the two models. Both simulations ha ve the fluid speed at the nozzle face of V = 0.01 m/s. However, the flow rates at the noz zle face are different due to different total nozzle face area (for the axisymmetric mode l, the actual nozzle face is a cylindrical surface which has the area of 12 times of the area of the nozzle face of the 3D model, a flat circle). Also note that Figure 5.6a only shows temp erature distribution on the symmetry plane of the 3D model whereas the plot in Figure 5.6b can be of any crosssection through the axis of the tank. In Figure 5.6a, heat diffusion dominates in the region on the right and under the pumpnozzle unit with a clear temperature gradient from the tank wall whereas the rest has lower temperat ure due to convection heat transfer as discussed previously. In Figure 5.6b, the temperature dist ribution for the axisymmetric model is totally different. Temperature is distributed more uniformly since the larger flow rate from the nozzle yields better mixing ove r the entire region. Due to the axisymmetry of the model, the fluid flow discharged from the nozzle face after impinging on the evaporator section of the heat pipe can onl y flow in two directions: going up along the heat pipe up to the top of the tank or going down along the axis of the tank in an axisymmetric manner (annular flow wrappi ng around the heat pipe). Low temperature fluid is confined in a small region next to th e heat pipe, especially the portion right under the spherical tip. Overall temperature is hi gher than that for the 3D model. Average
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88 speed, taken over the entire computational domain, can be used as a parameter for assessing the mixing effectiveness, which plays a role in leveling the temperature difference in the fluid. Figure 5.7 shows how the fluid sp eed at nozzle face affects the mixing effectiveness. As the speed at nozzle increases, the average speed also increases linearly for both 3D and axisymmetric models The rate of increasing average speed for the axisymmetric model is much higher than that for the 3D model (about 4 times), meaning that the axisymmetric model has be tter performance in mi xing effectiveness. The value of average speed for axisymmetr ic model (ranging in about 0.002.012 m/s) is always higher than that for 3D model (r anging in about 0.001.003 m/s) as expected because of higher flow rate from the nozzle as discussed above. The leveling of temperature difference it self can be assessed by observing the maximumtoaverage temperature differen ce, which is convenient for comparison between models (e.g. 3D model vs. axisymme tric model) despite different temperature ranges. Figure 5.8 shows the dependency of the maximumaverage temperature difference on the fluid speed at the nozzle f ace. As the speed at the nozzle increases, the temperature difference decreases for both mode ls with much higher drop rate (about 4 times) for 3D model (from 1.4 K to 0.6 K) compared to that for the axisymmetric model (from 0.4 K to 0.3 K). This means that the 3D model is more sensitive to the increasing of the speed at nozzle but the lower values of temperature difference confirms that the axisymmetric model gives better mixing effectiveness. For a ZBO system, the maximum temperature is the most important parameter indicating if evaporation can ha ppen, or ZBO effectiveness. Figure 5.9 shows the maximum temperature as a function of flui d speed at the nozzle for both models.
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89 (a) 3D model, simulation case 1 (b) Axisymmetric model, simulation case 6 Figure 5.6 Comparison of temperature distribution on symmetric plane, K 0 2 4 6 8 10 12 0.010.020.030.040.05 Speed at nozzle, m/sAverage speed, 103 m/s 3dimensional Axisymmetric Figure 5.7 Effect of fluid spee d at nozzle face on average speed
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90 0.2 0.4 0.6 0.8 1 1.2 1.4 0.010.020.030.040.05 Speed at nozzle, m/sMaximumAverage Temperature Difference, K 3dimensional Axisymmetric Figure 5.8 Effect of fluid sp eed at nozzle face on maximumaverage temperature difference 18 19 20 21 22 23 24 0.010.020.030.040.05 Speed at nozzle, m/sMaximum temperature, K 3dimensional Axisymmetric Figure 5.9 Effect of fluid speed at nozzle face on maximum temperature
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91 As the speed at nozzle increases, the maximum temperature decreases nonlinearly but monotonously. This yields an important conclusion that increasing the fluid speed discharged at the nozzle face improves the ZBO effectiveness. From a theoretical point of view, the problem under study can be approxima ted by the problem of heat transfer for constant freestream velocity and surface temp erature, a simpler yet well studied problem whose solution and discussion can be found in the textbook by Kays et al. (2005) with a result that the Nusselt number (representing the heat transfer coefficient) is proportional to a positive power of the Reynolds number (re presenting the freestream velocity). This means that as the forced velocity from the no zzle increases, the heat transfer coefficient on the surface of the evaporator section of the heat pipe incr eases and the flow transports the heat leak through the tank wa ll to the heat pipe by forced convection more effectively, thus the temperature rise in the fluid decreases. The maximum temperature in the 3D model is found much lower than that in the axisymmetric model, meaning that it has bett er performance in ZBO effectiveness. This is an interesting observation: the use of one pumpnozzle unit (3D model) gives better ZBO effectiveness than the us e of infinite number of pump nozzle units (axisymmetric model). One of the possible reasons is that many pumpnozzle units in the axisymmetric model give off more heat than a single unit in the 3D model, thus the higher maximum temperature for the former. However, the heat generated by the pump motor(s) may not produce that much effect. The reason for that may very likely be due to the limitations of the axisymmetric model itself. For an actual design of multi pumpnozzle units, there are always gaps between the units that may a llow complex 3D fluid flows and induce more mixing in the fluid, increase convective h eat transfer, and thus reduce temperature.
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92 5.4 Conclusions The numerical simulations give better unde rstanding of the fluid flow and heat transfer phenomena in more realistic 3D space needed for the design of a cryogenic storage tank for liquid hydrogen. Most parts of the forced flow from the nozzle, wrapping around the evaporator section a nd being cooled down there, can easily reach the opposite tank wall and carried the penetr ating heat away by convection over a large area of the tank wall before being recollected at the suct ion opening. The minor part of the incoming flow impinging on the evaporator section and re turning to the suction opening is the most ineffective one, since it has hardly touched the tank wall where the heat is penetrating. The collective outcome of this flow pattern results in better c ooling performance. There are three hot regions extended inward from the interface of the fluid with the tank wall. From top to bottom and also to the increase of size, the first one is projected above the opening of the suction tube; the second one is at middle of the cylindrical shell of the tank, by the side of th e pump; and the third on e is at the bottom of the tank, about 45 degree to th e back of the pump. They are connected by a large but thin high temperature area that covers the part of the tank wall on the back of the pump. These locations are important to the design of the storage system, e.g. suggesting the use of additional equipment for local treatments to el iminate the hot regions in order to increase ZBO effectiveness, or locating where to put thermal detectors for a control system to prevent the maximum temperature to exceed a preset threshold. In comparison to the 3D model, the solution on the axisymmetric model gives a distribution of higher temperatur e over the entire domain. It is found that the use of a single pumpnozzle unit in the tank, as simulate d in the 3D model, results in better ZBO
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93 performance than the use of an array of ma ny (infinite) pumpnozzle units, as simulated in the axisymmetric model. This happens becau se the fluid in a real 3D flow can move in all directions and through the gaps betw een pumpnozzle units to connect different parts of the tank whereas the nature of the axisymmetric model is to separate the fluid into regions blocked by solid walls. The minor part of flow impinging on the heat pipe then return without sweeping the tank wall, which is the mo st ineffectiveatcooling one in 3D model is the major part in the axisym metric model, resulting in higher temperature overall and thus less ZBO effectiveness for the axisymmetric model. The results from the simulations for both models show that the increasing of the fluid speed discharged at the nozzle face im proves both mixing effectiveness and antiboilingoff effectiveness. The numerical modeling and simulation can be satisfactorily used in the design of these systems to obt ain good predictions ove r a wide range of design alternatives and operating conditions.
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94 Chapter 6 Transient Analysis of Heat Transfer in Cryogenic Liquid Hydrogen Tank with Heat Pipe and Axial PumpNozzle Unit 6.1 Problem Description This study considers a cylindrical tank w ith spheroidal top and bottom as shown in Figure 6.1. The tank wall is made of aluminum covered by a multilayered blanket of cryogenic insulation. The tank is connected to a cryocooler via a heat pipe to dissipate the heat leak through the insulation and the tank wall into the fluid w ithin the tank. The condenser section of the heat pipe dissipates heat to the cryocooler while the evaporator section picks up heat from the fluid within the tank. The hot fluid is directed onto the evaporator section of the heat pipe by a fl uid circulation system within the tank. This system consists of a pump, a spray head fo r discharge of fluid and a collector tube feeding to the pump. Normally, the pump doe s not work until the maximum temperature inside the tank reaches a threshold, which is the boiling temperature of liquid hydrogen under the working pressure of the tank. When the fluid reaches the temperature threshold, the pump starts running and the nozzle discharg es the heated fluid onto the cold surface of the evaporator section thus cool the fluid off. After a certa in period of time, it shuts off and stands by until the fluid reaches the thresh old again. Only the fluid inside the tank is modeled for computation. The symmetry of the computational domain suggests the use of an axisymmetric model which consumes less computing resources compared to that for the original threedimensional problem. An axisymmetric model of the fluid inside the storage tank is presented in Figure 6.2. The essential dimens ions are denoted in general
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95 form as capital letters with the va lues assigned for this study given in Table 6.1. The axis of the tank is shown as the centerline coincident with the z axis. The cylindrical wall and the ellipsoidal top and bottom are shown as a st raight line and two elliptic arcs. The heat pipe is located along the cen terline and has the evaporat or and condenser sections. Table 6.1 Numerical values of fixed dimensions in Figure 6.2b Dimension A B C D E F G H L M N P R Value, m 1.50 0.65 1.300.100.300.100.201.500.300.10 0.05 0.300.10 The constant fluid propertie s were taken at a referen ce temperature of 20.3 K as: = 70 kg/m, = 12 6 Pa.s, cp = 10 kJ.kg .K k = 0.1 W.m .K The heat leak into the fluid is represented as a heat flux of qwall = 1 W/m uniformly distributed over the tank wall. The temperature on the surface of the evaporator section of the heat pipe is Tcool = 20 K. The normal speed at the nozzle face is a function of temperature as: otherwise 0 stop hour then 1 for run K, 23 ) max( start when m/s 08 0 T V (6.1) 6.2 Computational Model 6.2.1 Governing Equations The Reynolds decompositions approach with a mixing length turbulence model is used for modeling the fluid flow and heat transfer. The governing equations representing the conservation of mass, momentum, and ener gy for steady state fl ow of liquid hydrogen in the tank as an incompressible fluid of constant properties in microgravity condition can be written for the axisymmetric model as: 0 1 z u ru r rz r (6.2)
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96 Cryocooler Heat exchanger Controller Solar array Pumpnozzle unit Tank wall Insulation Heat pipe Liquid cryogen Radiator Condenser Evaporator Heat flux from surroundings Figure 6.1 Schematic of cryogenic storage system with axial pumpnozzle unit (a) Threedimensional arrangement (b) Axisymmetric model and dimensions Figure 6.2 Threedimensional domain and simplified axisymmetric model
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97 2 21z u ru r r r r p z u u r u u t ur r r z r r r (6.3) 2 21z u r u r r r z p z u u r u u t uz z z z z r z (6.4) 2 21z T r T r r r k z T u r T u t T cz r p (6.5) 6.2.2 Boundary Conditions The boundary conditions on velo city and temperature are On nozzle face: V u uz r 0 (6.6) On centerline: 0 0 r u uz r (6.7) On all solid interfaces: 0 z ru u (6.8) On tank wall: wallq n T k (6.9) On evaporator section: coolT T (6.10) On other boundary surfaces: 0 n T (6.11) 6.2.3 Numerical Solution The governing equations and boundary conditions, Equations (6.2) to (6.11), were solved numerically as discussed in section 2.4. Figure 6.3 shows the mesh of about 10000 quadrilateral elements for the axisymmetric m odel. To solve the finite element equations, the fully coupled successive substitution algo rithm was employed with the tolerances of 0.0001 and 0.01 for the relative error and resi dual convergence crite ria, respectively.
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98 Figure 6.3 Quadrilateralelement mesh for axisymmetric model of storage tank with heat pipe and axial pump nozzle unit
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99 6.3 Results and Discussion The transient solution for this problem can be presented in several stages: initially, the fluid is stationary and has a uniform temperature of 20 K; stage 1: the stagnant fluid is heated up by heat co nduction only, until the maximum temperature reaches 23 K; stage 2: the pump starts 1hou r run and creates a forced flow from the nozzle, heat transfer incl udes conduction and convection; stage 3: the pump stop, but there still fluid flow as the result of stage 2, heat transfer also includes conduction and convection until the entire fluid becomes s till after a long enough time. Stages 2 and 3 compose a cycle with a runinterval (stage 2) and restinterval (s tage 3). The following cycles are similar to the first one. Figure 6.4 presents the temperature distri bution at the end of stage 1 (after 83 hours) when the maximum temperature reaches 23 K. It shows the conduction pattern with temperature decreasing gradually from the heated surface (tank wall) toward the cold surface (evaporator section of the heat pipe) and separate d into isothermal layers. It can be observed that the inside isothermal la yers tend to round off at the corners of the tank, shared by the cylindrical shell and th e spheroidal top and bottom, with more uniform changes of curvature, thus the geom etric shape of the tank is not thermally conformal at the corners where the spots of maximum temperature are located. A sensor is needed to monitor the temp erature there and give a signal to turn on the pump if the temperature exceeds a certain threshol d (23 K). That finishes stage 1. Figure 6.5 shows the changes of maximum a nd mean temperatures of the fluid in stage 1 as functions of time. The mean temp erature increases linearly while the maximum temperature increases at a hi gher rate and mostly nonlinearl y during several first hours.
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100 Figure 6.4 Distribution of temperature at the end of stage 1, K 20 21 22 23 020406080 Time, hoursTemperature, K Maximum values Mean values Figure 6.5 Maximum and mean temper atures vs. elapsed time, stage 1
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101Figure 6.6 present the distributions of fl uid flow and temperat ure at the beginning (5 minutes) and Figure 6.7, at the end (60 minutes) of stage 2. In Figure 6.6a, when the pump has just st arted for a few minutes, the fluid flow from the nozzle reaches the evaporator secti on, cool off the fluid along the way and flow along the length of the heat pipe up to the top of the tank then follows the curvature of the tank shell, sweeps through the top and the cyli ndrical shell, increase s the heat transfer with the tank wall. The lower part of the ta nk is still unperturbed ma king it harder for the flow to displace the stagnant fluid there due to the lack of momentum of the flow since it is now far away from the nozzle. The flow is forced to separate from the wall and direct toward the suction tube of the pump, making a closed streamline. The fluid inside the streamline directly driven by the jet from th e nozzle is also affected by viscous effects and creates a family of streamlines. As the re sult of such flow pattern, the temperature distribution shown in Figure 6.6b has a high temperature region next to the bottom and gradually decreases upwardly and inwardly from the lower corner of the tank. The location of maximum temperature moves from the lower corner toward the bottom. After 1 hour running of the pump, the veloc ity field is getting to steady state and has the distribution as shown in Figure 6.7a. The fluid mixing is better resulting in much more uniform temperature field as shown in Figure 6.7b (note that a shorter temperature range is used to better visualize the temper ature distribution) where the high temperature region is pressed to the wall and remains in a thin layer. The maximum temperature spot is now at the middle of the bo ttom (on the centerline) where th ere is a stagnant zone since the fluid flow collected to the suction tube cannot reach that spot. The pump shuts down that ends stage 2.
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102 (a) Streamlines and speed, m/s (b) Temperature, K Figure 6.6 Distributions of velocity and temperature, stage 2, 5 minutes (a) Streamlines and speed, m/s (b) Temperature, K Figure 6.7 Distributions of velocity and temperature, stage 2, 60 minutes
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103 For quantitatively assessing the effect of fluid mixing by the pump to temperature distribution, Figure 6.8 shows how maximum and mean temperatures decrease over time. Mean temperature decreases gradually. Maximu m temperature decreases slowly at first, then drops at a higher rate, and then slows down a bit at the end. The drop of maximum temperature in this stag e is about 2 K in 1 hour. 20.5 21 21.5 22 22.5 23 0102030405060 Time, minutesTemperature, K Maximum values Mean values Figure 6.8 Maximum and mean temper atures vs. elapsed time, stage 2 Figure 6.9 shows the temperatur e distribution at the end of stage 3. The pattern is different than that at the end of stage 1 since there still sl ow circulations remains even though the pump has been off for some time, t hus there are convective heat transfer that make it different than stage 1. The location of maximum temperature in this pattern is at the middle of the cylindrical sh ell of the tank wall. Temperature has to be measured at this location by another sensor to control the switching on operation of the pump every time the temperature there ex ceeds the threshold of 23 K.
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104Figure 6.10 presents the maximum and mean temperatures during stage 3, which is somehow similar to that of stage 1 alt hough the numerical values are different. The mean temperature still increases linearly and the maximum temperature, nonlinearly, fast rate at the beginning then sl ows down. However, it takes only about 70 hours for the fluid to heat up to a maximum temperature of 23 K again (compare to 83 hours in stage 1). This happens because the temperature at the be ginning of stage 3 is higher than that of stage 1 as represented by mean and maximum temperatures in Figure 6.10 and Figure 6.5. This also implies that each of the follo wing cycles will end at higher temperature and thus becomes shorter than th at of the previous one. Figure 6.11 shows the maximum and mean temperatures over se veral cycles. It can be observed that their change follows some determined rules. In the runinterval of 1 hour, both temperatures dr op but not as much as in the prev ious cycle. The result is the restinterval is getting shorte r as the number of cycles increases. We can estimate the time when this type of cycle (1hour runinterval, in restinterval until maximum temperature reaches 23 K) stops working. By means of extrapolation the maximum temperature at the end of each runinterv al, it is found that af ter about 337 hours (14 days), the restinterval will vanish, i.e. th e pump has to run for a much longer time to reduce the maximum temperature to some reas onable level that keeps the restinterval longer in the order of tens of hours. 6.4 Conclusions The numerical simulations provide insight ful understanding of the phenomena of transient fluid flow and heat transfer in an active circulat ion cryogenic storage system for liquid hydrogen. Since there are several differe nt flow patterns corresponding to different
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105 stages created by the intermittent operation of the pump, there are different temperature distributions that characterize each stage. As a result, the location of maximum fluid temperature moves from place to place: at the tank corners for the stagnant fluid during stage 1; at the middle of the bottom when the pump is running (stage 2); and at the middle of the cylindrical shell when the pump is off but there are still fluid circulations due to residual momentum (stage 3). These pr edictions are essential for the design of the system as locating the temperature sensors at the spots of highest temperature is required. These sensors will provide feedback to the control circuit for the operation of the pump motor. The use of many temperature sensor s may complicate the system a bit but having all critical locations monitored ensures a safe r and more effective operation of the system. The pump operation cycle with runinterval s of constant time and restintervals controlled by an upper threshold temperature can work only for a short time plan (less than 2 weeks for the specific pl an considered in this study). For longer term applications, different pump operation schemes are needed Based on the results found in this study, several modified pump operation cycles can be proposed. One potential plan is that the runinterval is set to increase from cycle to cycle (the lengths of tim e of the runintervals are precomputed by using numerical simulati on) so that the pump will run long enough to keep the restinterval from getting shortened. Another plan is that the runintervals are controlled by a lower threshold temperature (that is, the pump is set to run until the fluid maximum temperature reaches a lower thres hold). The maximum temperature in the runinterval (stage 2) has been predicted to lo cate at the middle of the tank bottom. Another sensor will be needed here to detect the te mperature lower threshold. Transient analyses for the proposed schemes are necessary to conclude their feasibility and effectivity.
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106 Figure 6.9 Distribution of temperature at the end of stage 3, K 20 21 22 23 0102030405060 Time, hoursTemperature, K Maximum values Mean values Figure 6.10 Maximum and mean temper atures vs. elapsed time, stage 3
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107 20 21 22 23 04896144192240288336 Time, hoursTemperature, K Maximum values Mean values Extrapolation Figure 6.11 Maximum and mean temperatur e vs. elapsed time for first 3 cycles
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108 Chapter 7 Analysis of Cooling Performance in Refrigerated Warehouse with Ceiling Type Refrigeration Units 7.1 Problem Description This study considers a typical refr igerated warehouse as shown in Figure 7.1. A set of many cooling units (CU) is installed along the front wall in front of the arrays of product packages, to provide cold air flow th at maintains low temperature in the space. The products are stacked on pallets into many pa rallel arrays with wide aisles between one another and clearances from the walls a nd from the floor. Each array consists of 2 backtoback rows of 4 piles of 3 stacks of packages with clearances between each other, both horizontal and vertical, as suggested by guidelines (IIR, 1966). This arrangement in the warehouse possesse s two parallel plan es of symmetry as shown in Figure 7.1. The first one cuts through th e middle of an array and separates its two rows of stacking packages. The second one cuts through the middle of an aisle between two arrays. The space contained between the two planes of symmetry represents almost the whole space inside the refriger ated warehouse (without taking into account the endwall effects) by mirroring itself through th e planes of symmetry to recreate the whole space. The 2D and 3D models for the refrigerated warehouse are shown in Figure 7.2. For 2D simulations, the computational domain is modeled as a rectangular region shown in Figure 7.2a containing 12 product packages st acked with vertical and horizontal gaps between them to separate them from each othe r and from the floor and the back wall. In
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109 front of the array located a CU which blows the cooling ai r through its outlet on the right face. The relevant lengths L1 through L11 are given in Table 7.1. The values of L5L8 were chosen in accordance with the available guidelines (IIR, 1966; Tressler et al., 1968). The CU location is defined by the distance X from the front wall and the height Z from the floor. This 2D model represents the space in the warehouse on a vertical plane cutting through the CU and th e arrays of packages. For 3D simulations, the space between the two planes of symmetry is modeled as a box region as shown in Figure 7.2b including a half of an aisle, one row of four piles of three stacks of product packages, and a set of a large number of CU in front of the array of pack ages modeled as one long CU. The relevant dimensions for the 3D model ar e the same as the respective ones for the 2D model. In the y direction that is absent from the 2D model, the widths of a package and of the computational domain ar e 1.0 m and 2.0 m, respectively. Table 7.1 Numerical values of fixed dimensions in Figure 7.2a Dimension L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 Value, m 7.0 4.0 1.2 0.8 0.1 0.1 0.2 0.1 0.4 0.6 0.4 Several factors may affect the thermal beha vior of the warehouse such as cooling air velocity and temperature; location of th e CU, both horizontal and vertical; and product distribution pattern, i.e. cleara nces between racks, aisles, et c. This study investigates the effects of the blowing air velocity and the location of the CU. Simulations with 3D and 2D models with base settings are run and the results are compared to justify the use of the 2D model. For a parametric analysis, a dditional 2D simulations with five different blowing velocities and ei ght different CU locations are then performed.
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110 Figure 7.1 Basic arrangement in a refrigerated warehouse
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111 (a) Twodimensional model (b) Threedimensional model Figure 7.2 Twoand threedimensional models for refrigerated warehouse
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112 The simulation cases are summarized in Table 7.2. For simulation cases 2, the CU is fixed at the base location whereas the blowing air velocity V varies. For simulation cases 8, the blowing air velocity V is fixed whereas the CU location varies. Pseudodirection codes NE, NW, SE, SW, N, S, E, and W (Figure 7.2) are used to indicate the location of the CU relative to the base (central) location dependent on X and Z Table 7.2 Simulation cases for refrigerated warehouse Case # CU location X m Z m V m/s ModelNotes 1 Central 1.1 3.3 0.50 3D Base case 2 1.1 3.3 0.50 2D 3 1.1 3.3 0.25 CU fixed, V varied 4 1.1 3.3 0.30 " 5 1.1 3.3 0.40 " 6 1.1 3.3 0.75 " 7 1.1 3.3 1.00 " 8 NE 1.3 3.5 0.50 V fixed, CU moved 9 NW 0.9 3.5 0.50 " 10 SE 1.3 3.1 0.50 " 11 SW 0.9 3.1 0.50 " 12 N 1.1 3.5 0.50 " 13 S 1.1 3.1 0.50 " 14 E 1.3 3.3 0.50 " 15 W 0.9 3.3 0.50 "
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113 The applicable thermal properties for air are taken from Kays et al. (2005) at a reference temperature of Tref = 0C and listed as follows: = 1.293 kg/m, = 17.2 6 Pa.s, k = 24.07 W.m .K cp = 1004 J.kg .K = 3.6633 K Gravitational acceleration is taken as g = 9.8 m/s. The thermal properties for the products are adapted from ASHRAE (2002) as s = 840 kg/m, ks = 0.52 W.m .K cp ,s = 3.793 J.kg .K The temperature at the outlet side of the CU is fixed at a constant temperature of Tcool = 0C, so chosen for the refrigerated space to achieve the range of temperature proper for the storage of foods such as fr esh fruits and vegetables, poultry and dairy products, etc. as recommended in ASHRAE (2002) and Hardenbur g et al. (1986). The linear heat transfer models whose relevant data are taken from ASHRAE (2002) are applied for the floor, the ceiling and the walls. wh ere the floor is assumed to be made of 6 in. (0.152 m) concrete uninsulat ed slab under ground temperature of Tgnd = 15C with a constant heat transfer coefficient of hCF = 1.18 W.m .K ; the walls and the ceiling are both made of 4 in. (0.102 m) polyuretha ne insulation under outside or ambient temperature of Tamb = 35C, with a constant h eat transfer coefficient of hPU = 0.23 W.m .K There is also a lightings load of qlight = 10 W/m, as recommended in IIR (1966), that can be considered as a uniform heat flux adde d to the heat flux through the ceiling. It may be noted that moisture content (humidity ratio) of the air in a refrigerated space is expected to be fairly low and theref ore, the water vapor in the air has not been included as a part of the simulation model. In addition, the mode l considered only the steadystate operation of the warehouse and t hus did not include periodic maintenance operations such as defrosting of the cooling coil.
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114 7.2 Computational Model 7.2.1 Governing Equations The Reynolds decompositions approach with a mixing length turbulence model is used for modeling the air flow and heat transf er. Steady state, incompressible flow of air is considered. The fluid properties were take n as constants except the varying density for buoyancy term in the momentum equation. Th e equation for the conservation of mass, momentum, and energy can be written for the 3D model in rectangu lar coordinates as: 0 z u y u x uz y x (7.1) 2 2 2 2 2 2z u y u x u x p z u u y u u x u ux x x x z x y x x (7.2) 2 2 2 2 2 2z u y u x u y p z u u y u u x u uy y y y z y y y x (7.3) ref 2 2 2 2 2 2T T g z u y u x u z p z u u y u u x u uz z z z z z y z x (7.4) 2 2 2 2 2 2 pz T y T x T k z T u y T u x T u cz y x (7.5) 7.2.2 Boundary Conditions The boundary conditions on velocity are On CU outlet: 0 z y xu u V u (7.6) On planes of symmetry: 0 yu (7.7) On all solid surfaces: 0 z y xu u u (7.8) The boundary conditions on temperature are
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115 On CU outlet: coolT T (7.9) On floor surface: T T h n T k gnd CF (7.10) On wall surfaces: T T h n T k amb PU (7.11) On ceiling surface: light amb PUq T T h n T k (7.12) On other boundary surfaces: 0 n T (7.13) 7.2.3 Numerical Solution For each simulation, the governing equa tions along with the boundary conditions, Equations (7.1) through (7.13), were solved using the fini te element method as discussed in section 2.4. Figure 7.3 shows the mesh of about 6000 quadrilateralelement for the 2D model. It can be observed that the fine mesh of total thickness of 5 cm consisting of three layers with 1 cm thickness of the first layer concentrate along the fluidsolid interfaces, such as the floor, the ceiling, the walls, the cover and the inlet and outlet of the CU, and the gaps between the packages The remaining area is filled with square element of regular size of 10 cm 10 cm. The fully c oupled successive substitution algorithm was used to solve the finite element equations with tolerances of 0.0001 and 0.01, for the relative error and residu al convergence criteria, respectivel y. For the 3D model, a mesh of about 109000 eightnode hexahedral elements as shown in Figure 7.4 was used with the segregated algorithm to so lve the finite element equati ons with a tolerance of 0.001 for the relative error convergence criterion. It can be observed that the 3D mesh has the pattern on the plane of symmetry similar to that of the 2D mesh.
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116 (a) Full view (b) Expanded view of cooling unit (c) Expanded view of first package Figure 7.3 Quadrilateralelement mesh for 2D mode l of refrigerated warehouse with cooling unit and packages
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117 Figure 7.4 Hexahedralelement mesh for 3D model of refrigerated warehouse with cooling unit and packages
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118 7.3 Results and Discussion Figure 7.5 presents the solution of air velo city, pressure and temperature for the 3D base case (simulation case 1). Figure 7.5a shows the 3D streamlines of the air flow inside the warehouse as spatial curves originated from nine representative starting points distributed on a 3 matrix on the blowing opening of the CU. These streamlines are numbered from 1 to 9 with colorcoded legend for eas ily tracing their paths. Figure 7.5b presents the distribution of ai r speed by displaying respectiv e interpolated filled color on orthogonal slice planes. The slic e planes, selected in such a way that can reveal the structure of the volumetric data, include the pl anes perpendicular to yand zdirections and cutting through the center of the products. Parts (a) and (b) of Figure 7.5 can be examined simultaneously to construct the image of the flow field in the domain. The co ld air flow cooled by the coil on the suction side of the CU pulled by the fan blows into th e space at full speed of 0.5 m/s. Under the influence of the buoyancy effect, the colder air which has high er density goes down smoothly as shown in both parts (a) and (b) of Figure 7.5 for all streamlines. Most of this main flow drops down toward the floor but soon gets pulled back to feed to the suction side of the CU under the effect of lower pres sure there created by the fan. This forms a short circuit for most of the streamlines. The air speed in the short circuit zone is the highest in the whole domain (0.2 m/s and more ). This kind short circuit can be happening several times to a flow until it exits the CU at an "unfavorable" starting point. There, because the zone under the CU is already filled of shortcirc uit flows; the "unfavorable" flow is forced to go outside that zone, all the way down to the floor There it makes a turn to avoid the obstacles (the pr oduct packages) to the unoccupied zone in the aisle, sweeps
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119 through the floor until reaching the back wall then goes up, fills the space above the stacks under the ceiling and moves toward the CU to get forced down to the floor again and repeat the cycle until it get to a "favorab le" spot allow it to feed to the CU or its momentum got dissipated dry a nd it dies out at some stagnant point The flow along the back wall can never reach to the ceiling, leav es a still air zone th ere. Even though there are gaps between the packages and the floor and the wall as well as between themselves, the major flow mainly in favor of flowing in the open zone of the aisle at slow speed (about 0.1.2 m/s). However, there are also minor flows induced by natural convection due to temperature difference from the floor a nd the back wall that moves inside the gap next to the back wall as well as the gaps between the packages. Figure 7.5c presents the isosurface plot fo r pressure distribution. The value of air pressure is the same on an isosurface. It can be observed that most of the isosurfaces are almost flat, welllayered, and perpendicular to the vertical direction. This pattern implies that vertical flow is in fa vor thus natural convection domin ates the air flow field. The effect of forced convection (horizontal direct ion) can only be observe d in the region close to the outlet opening and the shor t circuit zone where the isosurfaces have high curvature. Figure 7.5d presents the slice planes plot of temperature distribution for simulation case 1. Wherever the air speed is hi gh, such as in the main air flow or in the circulations close to the exha ust opening, the temperature is lower due to low temperature in the supply air itself or by well mixing it with the heated air inside the room. The strong short circuit airflow creates a low temper ature zone around and under the CU where the cold air blows into the room and has not pick ed up much heat in the room yet. The first pile of product packages bene fit from this zone by heat c onduction from the products to
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120 the neighboring cold air resulting in low temper ature of about 1C in this pile. Similarly, the packages also have low temperature on th e aisle side because of lower temperature there (around 2C) due to the mixing effects by circulations of the velocity field. Since there is almost no flow near the floor under the packages, there is a high temperature zone there that includes the maximum temper ature. However, the air gap between the floor and the first stack of packages quite e ffectively prevents this high temperature on the floor to affect the products directly. Wh ile the maximum temper ature on the floor is about 89C, the highest temp erature on the bottom of these packages is only about 45C, which is still in the practical range fo r refrigerated warehousi ng. The heated up air on the floor forms some natural convection flows inside the vert ical gaps, thus transports some heat from the floor to the higher stack s and rises the temperat ure up to a few degree although not significantly since that is not capable of spreadi ng widely into the products. The still air under the ceiling towa rd the back wall results in a zone of higher temperature where its pattern shows that heat transfer is mainly by conduction. Figure 7.6 presents the air velocity field and the temperature di stribution for the 2D base case (simulation case 2). In Figure 7.6a, the streamlines of the airflow are plotted on the filled background with co lor representing the air speed The fan of the CU pulls the air through the coil banks to cool it down and blows the cooled ai r from its outlet into the refrigerated space. This cold airflo w has higher density compared to surrounding warm air thus it tends to go down and feeds back to the CU inlet because of the low pressure there created by the fan. This fo rms a major short circuit circulation under the CU. Because of the initial momentum, a part of the flow sweeps over the top of the stacks then returns to the inlet.
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121 (a) Streamlines (b) Speed, m/s (c) Pressure, Pa (d) Temperature, C Figure 7.5 Distributions of air velocity, pressure, and temperature for simulation case 1 (3D model, base case: X = 1.1 m, Z = 3.3 m)
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122 It can also be observed in Figure 7.6a that a minor part of the flow find their ways in the gap between the floor and the packages reaches the back wa ll and gets forced up by the natural convection of hot air at the back wall to retu rn to the CU inlet along the ceiling. In comparison to the 3D model, th ese observations predict the flow pattern accurately to some degree such as the short ci rcuit flows and the flow along the floor and the back wall. Figure 7.6b shows the distribution of air pressure for simulation case 2 in isobar contours. It can be observed th at this 2D pressure contour plot looks just like a cross section of the 3D isosurface pressure plot in Figure 7.5c cut by a plane perpendicular to the ydirection. This supports the similar pattern of the solutions from 2D and 3D models. In Figure 7.6c, the temperature distributi on inside the refrigerated space is represented by a filled color plot that shows different level of temperature in different regions of the domain. The circulation form ed by the combined effects of forced convection (due to the forced flow at the outlet and negative pressure at the inlet) and natural convection (due to buoyant force be cause of temperaturedependent variable density of air) creates a wellmixed region unde r the CU with uniform low temperature as the result. There is heat leak through the front wall, but the circulation of cold air is strong enough to sweep that wall and effectively removes the heat from it, leaving only floor and ceiling corners at sli ghtly higher temperature. Sin ce the second and third groups of circulation cannot reach the ce iling, especially in the part toward the back wall, with that much effectiveness, a st ill air region remains there, where heat conduction dominates with its pattern shown in Figure 7.6c.
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123Figure 7.6c also shows th at high temperature regions are found at back wall floor corner and its neighborhood as the h eat leak modeled by lin ear heat transfer coefficient comes through there without any si gnificantly strong air st ream to remove it. In comparison to the distribution of temperature for 3D model in Figure 7.5d, it can be seen that respective patterns are also very similar. The 2D distri bution of temperature can be considered as that on one ydir ection cross section of the 3D model. For assessing the cooling effectiveness a nd uniformity for the whole refrigerated space, we consider the following parameters: maximum temperature, mean temperature, and standard deviation of distributed temper ature around the mean temperature. The first two expresses how low the temperature can get which shows the e ffectiveness of the whole system. The last parameter represents the uniformity of temperature which is an important factor in refrigerat ion storage. Generally, the lower the temperature (maximum and mean) and standard devi ation, the better it is. The results of these parameters for simu lation case 1 (3D) and simulation case 2 (2D) are given in the first two rows of Table 7.3. The maximum temperatures for both are almost the same. The mean temperature for the 2D model is lower than that for the 3D model, whereas the standard deviation for 2D model is significan tly higher than that for the 3D model. This can be explained as that the 2D model implies that the packages are extended from one plane of symmetry to another one while the cold air supplied to both cases are at the same flow rate whic h leaves the 2D model less room volume to cool thus the lower mean temperature. Howe ver, the 2D model has no cooling from the side (aisle side) as the 3D model does thus the less unifo rmity or higher standard deviation.
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124 (a) Streamlines speed, m/s (b) Pressure, Pa (c) Temperature, C Figure 7.6 Distributions of air velocity, pressure, and temperature for simulation case 2 (2D model, base case: X = 1.1 m, Z = 3.3 m)
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125Figure 7.7 shows the distributions of maxi mum, mean, and standard deviation of temperature over the refrigerated space as f unctions of blowing air velocity for the simulation cases 1 with the CU at its base location. The maximum temperature occurred at the region on the floor under the third pile (t he second one from the back wall, Figure 7.2a). It can be obser ved that higher blowing air velocity will give lower temperature, both maximum and mean, and lo wer standard deviation. Therefore, the higher blowing air velocity is the better. Howeve r, in practice, the blowing air velocity is limited by equipment specifications and mo re importantly, cost effectiveness. Table 7.3 (from the second row down to the end for the results of 2D simulations only) shows how the CU locati on would affect the thermal effectiveness of the system, again with maximum and mean temperatures and standard de viation. It can be observed that the location SE (simulation 10 in Table 7.2) gives the lowest mean temperature and the lowest standard deviation, wher eas the location E (simulation 14 in Table 7.2) gives the lowest maximum temperature. Figure 7.8 presents the maximum temperat ure, the mean temperature, and the temperature standard deviation as functions of the CU location ( X and Z ) in the form of isotherm contours, which show the tendencies of these temperature parameters as the CU, moves away from the central (base) locati on. These functions ar e found by applying the cubic spline interpola tion method on the obtained data. It is observed that the maximum temperature, the mean temperature, and the st andard deviation decrease as the CU moves to locations E, S, and SE, respectively. Gene rally, the compromised direction to SE can be the best choice.
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126 0 1 2 3 4 5 6 7 8 9 10 0.20.40.60.81 Supply air speed, m/sTemperature, oC Max. temperature Mean temperature Standard deviation Figure 7.7 Effects of blowing air speed on temperature distribution (a) Maximum temperature, C (b) Mean temperature, C (c) Standard deviation, C Figure 7.8 Effects of cooling unit location on temperature distribution
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127Table 7.3 Effects of cooling unit location to temperature distribution CU location Max. temp., C Mean temp., C Std. deviation, C Central (3D) 8.80 2.17 1.13 Central (2D) 8.79 2.10 1.50 NE 9.20 2.58 1.53 NW 9.25 2.87 1.53 SE 8.71 1.47a 1.20b SW 9.10 1.78 1.51 N 9.08 2.63 1.50 S 9.47 1.60 1.26 E 8.47c 2.07 1.28 W 9.10 2.16 1.53 aLowest value of mean temperature among 2D cases. bLowest value of standard deviation among 2D cases. cLowest value of maximum temperature among 2D cases. 7.4 Conclusions Numerical modeling can be used conveniently to pred ict fluid flow and heat transfer and for the assessment of thermal uniformity in refrigerated warehouses. Instead of doing simulations by using expensive 3D models, proper 2D ones can be used to reduce computing cost while still producing us eful results that are accurate to some reasonable degree. This replacement is critic al where many design parameters and their interactions involve resulting in a large num ber of simulations required in limited time and computing resources that makes the us e of only 3D simulations impractical. As blowing air velocity from th e cooling unit increases, bett er cooling effectiveness and
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128 uniformity (lower maximum and mean temperat ure and lower standard deviation) can be achieved. The effect of the location of the cooling unit to temperature distribution is complicated with the interaction of positions in x and z directions. The best temperature range and uniformity can be obtained with th e CU moved toward the SE location. These results can be very useful for designi ng and operating refrigerated warehouses.
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129 Chapter 8 Analysis of Thermal Comfort Enhan cement by Using Ceiling Fan in AirConditioned Residential Room 8.1 Problem Description This chapter presents a study on thermal co mfort in a typical residential room as shown in Figure 8.1. The room includes an inle t (supply grille) and an outlet (return grille) for the airconditioning system, a ce iling fan suspended from the ceiling in the middle of the room with a light set attached to it, and a pe rson standing under the fan. A 2D model for the room is shown in Figure 8.2. The essential di mensions are denoted in general forms as L1 to L12. The numerical va lues used for the computations in this study are given in Table 8.1. The crossed regions that represent the person and the fanlights assembly are not part of the computationa l domain. The outer region around the person (enclosed by the dashed lines) of the widt h of L6 is a computational subdomain named Body used for assessing thermal comfor t factors in the surrounding air wrapping around the person thus expectedly give better evaluation of the comfort level of the person. The 2D model can approximate qui te well the transport phenomena at the symmetry plane. The data of imposed air spee ds and heat and mass fluxes are also taken equivalent values calculated such that the approximation takes into account the effects of finite dimensions of the solid surfaces (the person, fan, light, etc.) in the room. The forced flow from the ceiling fan is ch aracterized by the air velocity Vfan normal to the plane of the fan blades. The simulation cases are given in Table 8.2.
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130 Figure 8.1 Residential room with air conditioner and ceiling fan Figure 8.2 Twodimensional model of airconditioned room with ceiling fan
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131Table 8.1 Numerical values of fixed dimensions in Figure 8.2 Dimension L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11L12 Value, m 3.70 2.70 1.850.261.700.101.072.302.33 0.20 0.200.25 Table 8.2 Simulation cases for airconditioned room with ceiling fan Case # 1 2 3 4 Fan normal air speed Vfan, m/s 0 1.1 1.3 1.5 The supply air has a velocity normal to the opening with a speed of Vsupply = 1 m/s. Its temperature and contaminant concentration are Tsupply = 22C and wsupply = 0.0148 kg/kg air. The fan motor gives off a heat flux of qmotor = 10 W/m uniformly distributed on its cover. The light set under th e fan gives off a heat flux of qlight = 300 W/m. The outer surface of the person is cons idered of constant temperature Tbody = 34C and also giving off a mass flux of water vapor due to respiration and sweating of qw,body = 5 7 kg.m .s The constant fluid properties of air were taken at a reference temperature of Tref = 20C = 293.15 K as follows: = 1.2 kg/m, = 1.8 5 Pa.s, cp = 1004 J.kg .K k = 0.026 W.m .K = 0.0034 K and Dw/a = 2.5 5 m/s. 8.2 Computational Model 8.2.1 Governing Equations The Reynolds decompositions approach with a mixing length turbulence model is used for modeling the airflow and heat transf er. Steady state, incompressible flow of air as a multicomponent fluid that includes dry ai r and water vapor is considered. The fluid
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132 properties were taken as constants except th e varying density for buoyancy term in the momentum equation. The equation for the c onservation of mass for the air mixture (or carrying fluid), momentum, and energy and th e conservation of mass of water vapor can be written for the 2D model in rectangular coordinates as: 0 y u x uy x (8.1) 2 2 2 2y u x u x p y u u x u ux x x y x x (8.2) ref 2 2 2 2T T g y u x u y p y u u x u uy y y y y x (8.3) 2 2 2 2 py T x T k y T u x T u cy x (8.4) 2 2 2 2 w/ay w x w D y w u x w uy x (8.5) 8.2.2 Boundary Conditions The boundary conditions on velocity are On supply opening: 0 ,supply y xu V u (8.6) On fan blade surface: fan, 0 V u uy x (8.7) On all solid surfaces: 0 y xu u (8.8) The boundary conditions on temperature are On supply opening: supplyT T (8.9) On person surface: bodyT T (8.10)
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133 On motor cover surface: motorq n T k (8.11) On light surface: lightq n T k (8.12) On other boundary surfaces: 0 n T (8.13) The boundary conditions on water vapor concentration are On supply opening: supplyw w (8.14) On person surface: body w, w/aq n w D (8.15) On other boundary surfaces: 0 n w (8.16) 8.2.3 Numerical Solution For each simulation, the governing equa tions along with the boundary conditions, Equations (8.1) through (8.16), were solved using the fini te element method as discussed in section 2.4. Figure 8.3 shows the mesh of about 37000 quadrilateral elements for the 2D model. Parts (b) and (c) of Figure 8.3 give the expanded vi ew of the mesh at complex geometry boundaries. The fully coupled successi ve substitution algorithm was used to solve the finite element equations with to lerances of 0.0001 and 0.01, for the relative error and residual convergence criteria, respectively. After the solution of the primary variables (velocity, pressure temperature, and water vapor concentration) was found, relative humidity distribution was computed by using Equation (2.22). PMV value was calculated for a standing, relaxed person (wit h metabolic rate of 1.2 met) dressed in summer attire (with clothing insulation of 0. 5 clo) based on the data in the numerical solution, using Equation (2.25), and PPD value, using Equation (2.30).
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134 (a) Full view (b) Expanded view of fan motor/light region (c ) Expanded view of person's upper part region Figure 8.3 Quadrilateralelement mesh for 2D model of room with person and ceiling fan
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135 8.3 Results and Discussion Figure 8.4 presents the dist ributions of air velocity, temperature, and relative humidity for the base case, simulation case 1, when the ceiling fan is not in use. In Figure 8.4a, the velocity field is represented by th e streamlines on the filled background with the color proportional to air speed. The cool airflow ente rs the room through the supply diffuser on the left wall at uniform full speed V (1.0 m/s). The incoming flow goes straight horizontally at first since the temperature in the regi on far from the lights and the person has moderate low temperature that the buoyancy effect is insignificant. As the air flow approaches the middle part of the room where higher temperat ure distributed around the lights and the person is present, the buoyancy effect b ecomes stronger and tends to pull the main stream of the air flow down. However, since the inlet airflow has a quite high speed, a small part of the airflow splits up and continues to sweep along the ceiling at reducing speed before it goes down along the right wall to the outle t. The main stream goes down at the lights to the top of the pers on, sweeps through the upper part of him or her at a relatively high speed. Then the main stream splits again; the main part, still has momentum, bends to the left, sl ightly touches the floor and goes up, makes a clear strong circulation in the supply side of the room, the other part of the stream moves along the floor to the outlet at reducing speed. Figure 8.4b shows the distribution of te mperature for simulation case 1. The circulation in the supply side of the room creates a good mixing zone where the temperature is just about the inlet temperat ure or one, one and a half centigrade degree more. In the exhaust side of the room, si nce most of the streams with significant momentum just sweep along the ceiling, the wa ll, or the floor, the major region is left
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136 untouched or moving very slow. In this regi on, heat transfer is mostly occurring by diffusion. In Figure 8.4b, the core has a higher te mperature and it reduces towards the ceiling, the wall, and the floor, which shows a diffusion pattern. It can be also observed that there are thin layers of high gradient and high temp erature around the person and the lights, as well expected. Figure 8.4c is the plot of the distribution of relative humidity, one of the important factors for assessing thermal comfort. Relative humidity is a function of absolute pressure, water vapor concentra tion, and temperature. Its di stribution is computed from Equations 810. Since the gage pressure in th e room is found very sm all, on the order of 1 Pa, compared to the atmospheric pressure, on the order of 101 kPa, it has little effect on relative humidity. The water vapor concentration has some effect on relative humidity, but it is still small compared to the effect of temperature. The higher the temperature is, the lower the relative humidity gets, and vice ve rsa. This explains the somewhat identical pattern between the distributions of temperat ure and relative humid ity, except in opposite directions. Near the lig hts and the person, since the temperature is quite high, the relative humidity is low. The high relativ e humidity is concentrated in the supply side of the room where there is low temperature as the resu lt of the strong circ ulation as discussed previously. On the other hand, the exhaust si de of the room has lower relative humidity as the temperature in this region is higher. Figure 8.5 presents the dist ribution of air velocity, temperature, and relative humidity for simulation case 2 in which the cei ling fan is in use and it produces a normal (to blades plane) air speed of 1.1 m/s on the same order as the air flow through the supply inlet (1.0 m/s). In Figure 8.5a, the airflow field by st reamline contours plotted on color
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137 coded speed background. With th e presence of the velocity fro m the ceiling fan, the flow pattern is totally changed. The supply airf low is pulled towards the fan right after entering the room and creates a circulation si milar to that in the basic case, but much stronger. The supply side of the room become s very well mixed. But different than the basic case, the air velocity from the fan also creates a strong circul ation in the exhaust side of the room. However, there is no cool air supply on this side to induce the buoyancy effect, thus the circulation created by for ced convection is just circling at high region without touching the floor as th e circulation in the supply side does. There is also a weak stream sweeping along the floor to the outlet, si milar to the base case (simulation case 1). Figure 8.5b presents the dist ribution of temperature fo r simulation case 2. The wellmixed region in the supply side still has lower temperature as in simulation case 1. However, the air in the exhaust side of the r oom is also well mixed, but resulted in more uniformly distributed higher temperature co mpared to simulation case 1 since now the major means of heat transfer is convection. Only a small zone close to the floor still has the diffusion characteristics. Figure 8.5c shows the distribu tion of relative humidity for simulation case 2. This plot, again, shows how str ongly the relative humidity de pends on temperature in the room. The region in the exhaust side now ha s lower and uniform relative humidity, since the temperature is higher and uniform. The ai r in the supply side has higher relative humidity, since the temperature is lower. Howeve r, the relative humidity in this region is not as high as that in simula tion case 1, which suggests that the temperature in this zone is not as low as that in simulation case1. Therefore, it seems that the use of an additional ceiling fan increases the temperat ure in both sides of the room.
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138 (a) Streamlines and speed, m/s (b) Temperature, C (c) Relative humidity, % Figure 8.4 Distributions of velocity, temperature, and relative humidity for simulation case 1 (a) Streamlines and speed, m/s (b) Temperature, C (c) Relative humidity, % Figure 8.5 Distributions of velocity, temperature, and relative humidity for simulation case 2
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139 For a more detailed evaluation on how the air speed from the ceiling fan affect the local PMV values distributed around the person, Figure 8.6 shows a comparison of PMV distribution in the occupied site for simula tion cases 1 (no ceiling fan used) and 2 (with ceiling fan used). For simulation case 1, therma l comfort is at most satisfied (PMV = 0) over a large region on the right while it tends to be cooler on the left, especially on the upper part of the body of the person. For simu lation case 2, under the influence of the ceiling fan, the high PMV regions narrow dow n on both sides. The low PMV distribution implies that with the use of a ceiling fan, supply air temp erature (thus room temperature) can be increased but thermal comfort level is as satisfied as that for the case of no ceiling fan used. The above discussion on th e distribution of temperature, relative humidity, and the PMV (parts (b) and (c) in Figure 8.4 and Figure 8.5, and Figure 8.6) with in the room for two cases: with and without a ceiling fan is reasonable, in qualitative sense. Because of the low temperature of the s upply airflow, the air in one side of the room that near the supply grille has lower temper ature (thus higher relative hum idity and lower PMV) than the other part. However, fo r both cases, part (b) in Figure 8.4 and Figure 8.5 shows a difference of 3C between the two halves of the room separated by the person. This temperature difference is unrealistic and is th e result of the 2D simplification of a 3D flow situation. Since the width of the person is small compared with that of the room, the airflow supplied to the room is most likely going around the person by his or her side to flow toward the exhaust opening. This airflow plays an important role in convective heat transfer that keep the air in the room well mixed and having less temperature difference between two sides of the person.
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140 (a) Simulation case 1 (b) Simulation case 2 Figure 8.6 Comparison of PMV distribution between simulation cases 1 and 2
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141 The 2D model under study has no means to accommodate the airflow around the side and therefore it cannot describe the te mperature distribution accurately. In the 2D model, the shapes represented the body of the person and the fan motor/light assembly are the two obstacles extended through the whole depth of the model (in the direction perpendicular to the page). Therefore, the airflow is allowed to pass through only three gaps between the floor, the two obstacles, a nd the ceiling. The gap between the floor and the body of the person was designed in an attemp t to compensate this limitation so that the airflow around the side that is missing from the 2D model can be shared by two airflow ways on top and bottom of the body, not only the top one. Desp ite the limitation, a 2D model is less expensive to set up and to run simulations. On the other hand, with proper considerations, a 2D model can still give useful results. Although the 2D model has its limitation in describing the deta iled distributions of the fluid flow and temperature, thus the related parameters such as relative humidity and PMV, the average values of temperature an d relative humidity are in close range with the results from James et al (1996). Table 8.3 compares the ranges of temperature and relative humidity results from the 2D simulati ons to the typical values at satisfactory thermal comfort given in the energy simula tion and experimental study by James et al. (1996). The similar in ranges suggests that the use of average values from the numerical solution of the 2D simu lations is reasonable. Table 8.3 Comparison of temperature, rela tive humidity, and PPD for thermal comfort Temperature, C Relative humidity, % PPD, % Simulation cases 1 23.4.2 75 5 James et al. (1996) 25.6.7 60 10
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142Figure 8.7 presents the dependency of the mean temperature taken over the entire room as well as in the subdomain Body wh ich is a thin layer ar ound the person. It can be observed clearly that temperature does increas e as the result of the use of an additional ceiling fan in an airconditioned room in the entire domain as well as in the subdomain. More than that, as the air speed from the fa n increases, the mean temperature increases as well. This happens because the running ceili ng fan while increasing circulation brings down the still warm air under the ceiling and around the fan motor and keeps it circling inside the room without being effectively removed through the outle t and thus reduces the cooling effect of the increased air speed from the fan. At first this observation may raise the question of what is the point of using a ceiling fan if it makes people hotter instead of cooler. It is known that thermal comfort is dependent on temperature, relative humidity, and air speed (chilling effect). Th e thermal comfort factor should take into account the effects of the air speed around the person. The incr eases of mean air speed, especially in the subdomain around the person will have si gnificant impact on thermal comfort. PMV is the proper factor for the evaluation of thermal comfort in this situation. Figure 8.8 shows that PMV for the room is always lower than PMV for the subdomain Body. This implies that in a possible experiment if the measurements were not done close enough to the body the real PMV is al ways underestimated. As the air speed from the fan increases, PMV decreases in both domains. This decreasing trend is good for the cooling situation. If there are additional heat loads, the PMV curves will be shifted up, a decreasing trend is critical to keep the envi ronment within the comfort limits. If there is no additional heat load, the temperature setti ng for the airconditioner can be raised a few degrees for energy savings while the ceiling fan maintains the same comfort level.
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143 23 23.5 24 24.5 25 25.5 00.30.60.91.21.5 Fan Normal Air Speed, m/sMean Temperature, oC Room Body Figure 8.7 Effect of fan normal air speed on mean temperature 1 0.8 0.6 0.4 0.2 0 00.30.60.91.21.5 Fan Normal Air Speed, m/sPredicted Mean Vote (PMV) Room Body Figure 8.8 Effect of fan normal air speed on thermal comfort
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144Table 8.4 shows that the mean air speed increases as the normal air speed from the fan increases and the mean air speed valu es taken over the entire room are always higher than that taken over the subdomain Body around the person. Apparently, as the air speed from the fan increases, the mean air speeds also increase. The effect of the use of elevated air speed used to increase ma ximum temperature while maintaining thermal comfort for affected occupants is given in ASHRAE Standard 55 (2004, section 5.2.3, Figure 5.2.3). The data given in this standard applies to a lightly clothed person (clothing insulation 0.5.7 clo) engaged in near sede ntary physical activity (metabolic rates 1.0 1.3 met). Those ranges well cover the cases under investigation (0.5 clo, 1.2 met). Using the mean air speeds around the body to estimate the potential increa sed temperature, the standard shows that for simulation case 1, where the air speed is around 0.2 m/s, the offset temperature is almost negligible, while for simulation cases 2, where the air speed ranges in 0.4.6 m/s, the offset temp erature can reach up to 3C. For estimating the energy savings, the results from the study by James et al. (1996) show that an increase of 0.6C and 1.1C with fans in use from a ba se set point of 25.6C without fans yields to an average cooling energy savings of 2.6% and 14.9%, respectively. The above quantitative results confirm th e predictions made previously based on the PMV distribution contours (Figure 8.6) and the average value of PMV (Figure 8.8) in the occupied zone. Table 8.4 Effect of fan normal air speed on mean air speed in room and around person Fan normal air speed, m/s 0 1.1 1.3 1.5 Room mean air speed, m/s 0.235 0.571 0.652 0.743 Body mean air speed, m/s 0.223 0.459 0.567 0.634
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145 8.4 Conclusions The results from the numerical simulations provided a view of the fluid flow and heat transfer in a residential room with ai r conditioner and ceiling fan using a 2D model. Althought the 2D model cannot de scribe the fluid flow and h eat transfer within the space accurately due to its 2D simplification, with proper considerations, it gives qualititative assessment on the distributions of airflow, temperature, relative humidity, and PMV and quantitative assessment on their average values. For the base case where the fan is not in use, strong air circulations in the inlet side of the room keeps this side cooler due to convective heat transfer, while rather still air in the outlet side have the temperature di stribution pattern of diffusive heat transfer. When the fan is in used, strong circulations forced by the fan induces convective heat transfer that creates more uniform temperat ure distribution in bot h sides of the room. However, these circulations also reduce the to tal heat removal performance of the system by circulating the heat around the room instead of moving it to the outlet resulting in a slight rise of overall temp erature. The value of PMV calculated based on the average values of the relevant parameters (tempera ture, humidity, air speed) reflects better the condition of the person if the averaging is taken over the small region around the body rather than over the entire space (room). The former is higher than the latter about 0.5 on the ASHRAE thermal sensation scale (which is significant on a full scale from 3 to 3). As the air speed provided by the fan increase s, the PMV value decreases toward cooler side and thus overcompensates the temperature rise to leave more adjusting margin for a cooling situation, allowing higher heat load while maintaining the same level of comfort compared to that of the case where there is air conditioner only with no ceiling fan. Air
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146 speed from the ceiling fan of 1.1 to 1.3 m/s can allow an increase of temperature of the supply airflow from 22C (no fan in use) to about 25C. This ch aracteristic has good impact on cooling energy savings through the higher temperature set point for the air conditioning system. For a better analysis of the effects of the use of ceiling fans in an airconditioned room, 3D model is required. As a pilot pr oject, 2D modeling a nd simulation provides useful ideas and fundamentals for the devel opment of a 3D numerical model that can describe the space better and thus produce more accurate solution.
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147 Chapter 9 ThreeDimensional Analysis of Ther mal Comfort and Contaminant Removal in Hospital Operating Room 9.1 Problem Description This chapter presents a study on fluid fl ow and heat and mass (water vapor and contaminant gas) transfer in the air inside a hospital operating r oom and human thermal comfort and contaminant removal as the results. Figure 9.1a shows the basic setup in an operating room that includes a patient lying on an operating table with a surgical staff of four members standing around under a set of surgi cal lights. Fresh cold air is supplied to the operating room through two supply grilles located at high positions on the front (left) wall in order to remove the heat loads from the lights and the bodies of the occupants and contaminant, if any. Two exhaust grilles ar e located at low height on the opposite (right) wall. The occupants may give out water vapor due to respiration a nd evaporation on their skin. It is assumed that the patien t also gives out contaminant gas. An operating room of dimensions 6.1 m 4.3 m 3.0 m (20 ft 14 ft 10 ft) is considered. All the supply and exhaust grille s have the same size of 0.61 m 0.36 m (24 in. 14 in.). It can be observed that there is a plane of symmetry fo r the geometry of the room (and the subjects inside) as well as applicable physical conditions and boundary conditions. Due to this symmetry, only a ha lf of the room needs to be modeled. Figure 9.1b shows that the room in half is modele d as a threedimensi onal box (6.1 m 2.15 m 3.0 m) that has six boundary planes namely plane of symmetry, floor ceiling, and three walls (left, right and side walls). An x y z coordinate system is attached to the model with
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148 the origin located at the bottom left corn er on the plane of sy mmetry as shown in Figure 9.1b. The lying patient in half is modeled as a horizontal rectangul ar box (1.7 m 0.25 m 0.3 m) at the middle of the room. Its bottom surface that faces the floor represents the operating table, which is heat and mass insula ted. The other five surfaces model the body of the patient which is maintained at constant temperature Tbody = 34C and releasing water vapor and contaminant gas as constant fluxes qw,patient = 2.5 6 kg.m .s and qc,patient = 1 5 kg.m .s respectively. The standing staff members are modeled by the vertical rectangular boxes at both ends (staff members 1 and 2, both in half, 0.3 m 0.25 m 1.7 m) and by the side of the patient (sta ff member 3, in full, 0.5 m 0.3 m 1.7 m). Similar to the patient, the staff models are c onsidered as surfaces of constant temperature Tbody = 34C with a constant water vapor flux qw,staff = 4 6 kg.m .s but zero contaminant flux. The surgical light set is also modeled as a box (0.7 m 0.65 m 0.3 m) above the patient, whose bottom surface (f acing the patient) is defined as the lamp face entity, on which the major heat flux qlampface = 100 W/m goes through; and other surfaces are defined as the lamp back entity, on which a smaller heat flux qlampback = 5 W/m dissipates. Cool air is supplied to th e operating room through the supply opening at a forced speed of V = 1 m/s and temperature of Tsupply = 20C. Concentrations of water vapor and contaminant ga s in the supply air are wsupply = 0.01 and csupply = 0, respectively. The supply grille in the halfroom model is located at a high position on the left wall with its center at the coordinates YS (from the plane of symmetry) and ZS = 2.45 m (from the floor). The exhaust grille is at a low position on the right wall with its center at the coordinates YE (from the plane of symmetry) and ZE = 0.55 m (from the floor).
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149 (a) Basic arrangement (b) Computational model (halfroom) Figure 9.1 Threedimensional model of hospital operating room
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150 The effects of the horizontal locations of the supply and exhaust grilles ( YS and YE) are studied by running simulations with va rious combinations of these coordinates. Nine simulation cases are summarized in the first three columns of the first section of Table 9.1. Table 9.1 Simulation cases and comparison of results Air speed, m/s Temperature, C Relative humidity, % Case # YS, m YE, m OAa BZb OA BZ Ec OA BZ 1 1.5 1.5 0.12 0.11 23.2 23.0 22.4 58.1 58.9 2 1.5 0.5 0.11 0.10 23.2 22.9 22.4 58.2 59.2 3 0.5 1.5 0.12 0.10 22.4 22.3 22.3 60.8 61.0 4 0.5 0.5 0.12 0.09 22.4 22.4 22.4 60.6 60.7 5 1.0 1.0 0.12 0.14 23.6 23.4 23.0 56.5 57.2 6 1.0 1.5 0.12 0.14 23.6 23.4 22.9 56.6 57.3 7 1.0 0.5 0.12 0.14 23.5 23.3 22.9 56.9 57.6 8 1.5 1.0 0.11 0.11 23.3 23.0 22.4 57.8 58.7 9 0.5 1.0 0.12 0.10 22.3 22.3 22.2 61.0 61.1 Experimental data Mora et al. (2001) 19.5 24.5 Balaras et al. (2002) 18.6.5 27 Handbook/standard recommended conditions ASHRAE (1995) 20.4 50 aOverall bBreathing zone cExhaust
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151 For estimating the influen ce of these two factors ( YS and YE) on the responses of interest (CRE, PMV, etc.), the method of de sign of experiment (DOE) (Box et al, 2005) is adopted. Since the number of factors is only 2, full factorial designs is used for better design resolution. For twoleve l experimental design, two nu merical values (low and high levels) can be assigned to each factor to ge t a total of 4 experiments (simulations). For a threelevel experimental design, th ree numerical values (low, medium, and high) can be assigned to each factor to get a total of 9 experiments (simulations). The experimental values for both c oordinates are selected as: lo w = 0.5 m, medium = 1.0 m, high = 1.5 m. Simulation cases 1 respect to twolevel design, a nd simulation cases 1 for threelevel design. The constant fluid properties of air were taken at a reference temperature of Tref = 20C = 293.15 K as follows: = 1.2 kg/m, = 1.8 5 Pa.s, cp = 1004 J.kg .K k = 0.026 W.m .K = 0.0034 K Dw/a = 2.5 5 m/s, and Dc/a = 1.2 5 m/s. 9.2 Computational Model 9.2.1 Governing Equations The Reynolds decompositions approach with a mixing length turbulence model is used for modeling the air flow and heat transf er. Steady state, incompressible flow of air as a multicomponent fluid, which includes dr y air, water vapor, and a contaminant gas, is considered. The fluid properties were take n as constants except the varying density for buoyancy term in the momentum equation. The equation for the conservation of mass for the air mixture (or carrying fluid), moment um, and energy and the conservation of mass of each species can be written for the 3D model in rectangular coordinates as:
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152 0 z u y u x uz y x (9.1) 2 2 2 2 2 2z u y u x u x p z u u y u u x u ux x x x z x y x x (9.2) 2 2 2 2 2 2z u y u x u y p z u u y u u x u uy y y y z y y y x (9.3) ref 2 2 2 2 2 2T T g z u y u x u z p z u u y u u x u uz z z z z z y z x (9.4) 2 2 2 2 2 2 pz T y T x T k z T u y T u x T u cz y x (9.5) 2 2 2 2 2 2 w/az w y w x w D z w u y w u x w uz y x (9.6) 2 2 2 2 2 2 c/az c y c x c D z c u y c u x c uz y x (9.7) 9.2.2 Boundary Conditions The boundary conditions on velocity are On supply opening: 0 1 z y xu u u (9.8) On plane of symmetry: 0 yu (9.9) On all solid surfaces: 0 z y xu u u (9.10) The boundary conditions on temperature are On supply opening: supplyT T (9.11) On occupants surfaces: bodyT T (9.12)
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153 On "lamp face" surface: face lampq n T k (9.13) On "lamp back" surfaces: back lampq n T k (9.14) On other boundaries: 0 n T (9.15) The boundary conditions on water vapor concentration are On supply opening: supplyw w (9.16) On patient surface: patient w, w/aq n w D (9.17) On staffs surfaces: w,staff w/aq n w D (9.18) On other boundaries: 0 n w (9.19) The boundary conditions on contaminant concentration are On supply opening: supplyc c (9.20) On patient surface: patient c, c/aq n c D (9.21) On other boundaries: 0 n c (9.22) 9.2.3 Numerical Solution For each simulation in Table 9.1, a mesh of about 65000 hexahedral elements was generated. Three layers of refined elements of 1 cm height for the first layer and growth ratio of 1.45 are assigned along fluidsolid interfaces where high rates of momentum and heat transfer exist. The rest of the domain is filled with regular 10 cmsize cubeshaped
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154 elements. The supply and exhaust openings ar e mesh with the "map mesh" options at a finer element size to improve accuracy of th e air flow rate in and out of the operating room. The governing equations and boundary co nditions are solved numerically using the segregated algorithm with a tolerance of 0.001 for the relative error convergence criterion. The numerical so lution includes three veloci ty components, pressure, temperature, water vapor and contaminant co ncentrations. Relative humidity is computed by using Equation (2.22). Predicted mean vote (PMV) is computed by using Equation (2.25). To assess the performance of the vent ilation system of an occupied zone, the contaminant removal effectiveness (CRE) is us ed. The CRE factor involves the values of mean contaminant concentration at the supply and exhaust and in the breathing zone as (Hirnikel, 2002): S BZ S EC C C C CRE (9.23) For the present problem, the "breathi ng zone" as defined in ANSI/ASHRAE Standard 62.12004 as "the region within an occupied space between planes 3 and 72 in. (75 and 1800 mm) above the floor and more th an 2 ft (600 mm) from the walls or fixed airconditioning equipment". The "breathing zo ne" can be considered approximately the same as the "occupied zone" defined in ANS I/ASHRAE Standard 552004 as "the region normally occupied by people within a space, gene rally considered to be between the floor and 1.8 m (6 ft) above the floor and more than 1.0 m (3.3 ft) from outside walls/windows or fixed heating, ventilating, or airconditioni ng equipment and 0.3 m (1 ft) from internal walls" and the "sterile zone" as mentioned in (Mora et al., 2001) which covers the actual working space of the surgical staff.
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155 Figure 9.2 Hexahedralelement mesh for 3D model of hospital operating room
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156 9.3 Results and Discussion Figure 9.3 presents the distri butions of the variables of interest for simulation case 1. In Figure 9.3a, the distribution of air speed is displayed as re spective interpolated filled color on orthogonal slice planes. Th e slice planes, selected in such a way that can reveal the structure of the volumetri c data, include planes through the center of the grilles and the obstacles. Figure 9.3b shows the threedimensiona l streamlines which begin at nine representative starting points on the area of the supply ope ning. These streamlines are numbered from 1 to 9 with color coded legend for easily tracing their paths. Parts (a) and (b) of Figure 9.3 can be examined simultaneously to view the image of the flow field in the domain. The cold air flow enters the r oom at full speed (1 m/s) through the supply opening located at a high position on the left wall. Under the influence of the buoyancy effect, the colder air, having higher de nsity, goes down smoothly as shown in Figure 9.3b for all streamlines. While going down, the suppl y air flow is losing speed and spreading wider as it is reaching the floor. As the dr ive force due to the buoyancy effect depletes when the air flow touches the floor, it b ecomes influenced by lower pressure at the exhaust opening. Under this influence, most of the main air flow is pulled toward and exits through the exhaust openi ng at increasing speed in a curling move as shown in Figure 9.3b due to the nature of air flow of being not capable of ma king abrupt turns. A small part of the main air flow is influenced by complex drive force including the buoyancy effect in the hotter region close to th e occupants' bodies. This type of flow can go up and down and travels back and forth in the room, even between the bodies of the occupants, at lower speed It can be observed in Figure 9.3b that more disturbances (thus better air mixing) exist in the lower pa rt of the exhaust side of the room.
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157 (a) Speed, m/s (b) Streamlines (c) Pressure, Pa (d) Contaminant concentration, mg/kg air (e) Temperature, C (f) Relative humidity, % Figure 9.3 Distributions of air velocity, pressure, contaminant concentration, temperature, and relative humidity for simulation 1 ( YS = 1.5 m, YE = 1.5 m)
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158Figure 9.3c presents the isosurface plot fo r pressure distribution. The value of air pressure is the same on an isosurface. It can be observed that most of the isosurfaces are almost flat, welllayered, and perpendicular to the vertical direction. This pattern implies that vertical flow is of fa vor thus free convection domina tes the air flow domain. The effect of forced convection (horizontal direct ion) can only be observe d in the region close to the supply opening where the isosurfaces ar e no longer flat but having high curvature. There are also slight disturbances on the isos urfaces in the regions near the floor or nonslip interfaces (the bodies of the occupants). Figure 9.3d shows the slice planes plot for the distribution of contaminant concentration in the domain. Contaminant concen tration, considered to be released from the body of the patient at a constant rate, accu mulates inside zone 1, "microenvironment" (Woods et al., 1986), bounded by the surgical sta ff, the patient, and the surgical lights, where the air slightly moves. This contaminan t concentration, driven by the concentration gradient from the patient to the surrounding, transports mainly by di ffusion to the outside of the surgical field, and then get carried away by the fresh main air flow to the exhaust opening. The high contaminant concentration exis ts in the surgical site and the almost still air at the ceiling while the lower part of the room has low contaminant concentration. The pattern of diffusive tran sport (gradually varying con centration) can be observed between these two regions. Figure 9.3e is the slice planes plot of temperature distributi on for simulation case 1. Wherever the air speed is high, such as in the main air flow or in the circulations close to the exhaust opening, the temperature is lo wer due to low temperature in the supply air itself or by well mixing it with the heated air in side the room. The main air flow creates a
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159 low temperature region next to the supply opening where the co ld air enters the room and has not picked up much heat in the room yet. In the surgical field, heat released from the lights induces natural convection fl ows that carried the heat up to the ceiling, resulting in a region of higher temperature there. Such effect is less expressed around the occupants' bodies where the diffusion patte rn shows more clearly. The region of high temperature (24C and higher) spreads in the higher part of the room and covers most of the ceiling with not much uniform distri bution. The lower part of th e room has lower temperature (23C and less) but more uniform. The re gion of medium temperature (23C) dominates in the activity space of the occupants (at the height of 1 m). Figure 9.3f is the plot of relative humidity distribution, a key factor of thermal comfort. Relative humidity is a function of ab solute pressure, water vapor concentration, and temperature. Since the room gage pressu re was found very small (on the order of 1 Pa as shown in Figure 9.3c), compared to the atmos phere pressure (as high as 101 kPa), then it does not significantly affect the total (absolute) pressure, a nd thus almost does not affect the values of relative humidity. Wher ever low temperature and high water vapor concentration exist, relative humidity is high also. Near the surgical lights, the relative humidity is very low because of the high temperature. Inverse to the temperature distribution, high humidity region existed in the lower part of the room and low humidity existed in the higher part of the room. Mean values of air speed, temperature, and relative humidity can be used for a quick assessment of the thermal comfort condition of a room. The mean values are taken over both the entire domain (ove rallOA) and the occupied zone (considered the same as the breathing zoneBZ). For temperature, ther e are mean values taken over the exhaust
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160 opening area as well. Besides of being closer to thermal comfort conditions to the occupants, these mean values also show a cl earer trend of how they change as the design factors change. Table 9.1 shows a summary of these ba sic thermal comfort parameters for all simulation cases. For all simulations, the mean air speed varies in the range 0.10.14 m/s, about a tenth of the nominal supply speed ; the mean temperature varies in the range 22.2.6C (2C higher than the supply te mperature, 20C); the mean relative humidity varies in the range 57%. For each simulation, the difference of the mean air speed in OA and BZ is about 0.01.02 m/s, which is not a significant amount; the difference of the mean temperature in OA and BZ can be up to 0.3C, while the exhaust temperature can have a difference up to 0.9C, both cases are quite significant for thermal comfort; the difference of mean relative hum idity in OA and BZ is less than 1%. These observations suggest that for a simple assessm ent of thermal comfort, mean air speed and mean relative humidity taken over either OA or BZ can be used without much difference while it is best to use mean temperature taken over BZ since that is closer to the condition of the occupants. Temperature is obviously the most important criterion for a simple assessment of thermal comfort. In a cooling s ituation, the lower the temperature the better the thermal comfort condition is. It can be observed in Table 9.1 that the lowest mean temperature appears in the resu lts of simulation cases 3, 4 and 9 (22.3.4C in all three columns OA, BZ, and E). It occurs that fo r the minimum temperature case the exhaust temperature is very close to the bulk temperature (either BZ or OA) while it is not for the other cases. All of those simu lations (3, 4, and 9) have YS = 0.5 m. It is also found that the mean temperatures are very close within each of the following groups of simulations: {1, 2, and 8} (22.9.0C in BZ, YS = 1.5 m) and {5, 6, and 7} (23.3.4C in BZ, YS =
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161 1.0 m). The observation suggests that the ho rizontal location of the supply grille YS is highly significant to temperature and the smaller YS the cooler it is. This is apparently a fortunate case where the signifi cant effects of the factors ( YS and YE) to the response of mean temperature show explicitly on a ta ble which does not happen so often. A more systematic approach is to be introduced in later sections. Mean temperature and relative humidity are also compared with those fr om experimental data from actual hospital operating rooms reported by Mora et al. (2001) and Balaras et al. ( 2002) also given in Table 9.1. The data from these articles are collected from 2 and 20 operating rooms, respectively. The mean temperature and rela tive humidity from the numerical simulation shows reasonably good agreement with experi mental data. These mean computational values in all cases are also within th e recommended ranges specified by ASHRAE (1995). Figure 9.4 presents the computational re sults for simulation case 3, among the group of simulation cases with YS = 0.5 m that give the be st cooling performance as found previously. Parts (a) and (b) of Figure 9.4 for air speed and streamlines show that the supply air flow moves hor izontally without dropping down as in simulation case 1. This happens because of the heat released from the lights and occupants' bodies induces the natural convection flow wh ich forces the heated air up directly into the incoming supply main flow and supports it to m ove straight. The streamlines plot in Figure 9.4b also show that the supply air flow moves ar ound in the upper part and supply side of the room before exiting through the exhaust openi ng, resulting in bette r air mixing in this region. In this simulation, the exiting flow moves from far away straight to the exhaust opening without curling as s een in simulation case 1.
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162 (a) Speed, m/s (b) Streamlines (c) Pressure, Pa (d) Contaminant concentration, mg/kg air (e) Temperature, C (f) Relative humidity, % Figure 9.4 Distributions of air velocity, pressure, contaminant concentration, temperature, and relative humidity for simulation 3 ( YS = 0.5 m, YE = 1.5 m)
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163 The horizontal main air flow shows its effects explicitly in the pressure isosurfaces in Figure 9.4c. In the region dominate d by the horizontal flow (as the combination of forced and natural convection) in the supply side and close to the ceiling, the pressure isosurfaces have very high cu rvature, while in the natural convection (vertical flow) dominated regi on on the exhaust side, the pres sure isosurfaces have the horizontal flat plate form like simulation case 1. The slice planes plot for contaminant concentration in Figure 9.4d shows that the well mixed air region has positive effects on contaminant removal with a very low concentration. Contaminant is concentrated to ward the exhaust side of the room close to the ceiling where the air is almost still as shown in Figure 9.4b. From that region down toward the floor, the diffusion pattern shows since convection transport is limited in that region due to the lack of strong air flow. In comparison to simulation case 1 since there is stronger air flow reaching into the surgical fi eld, the contaminant in this region is less accumulated. However, convection transport leaves high contaminant concentration in front and on top of staff me mber 2 (standing on the exhaust side of the room) which should be taken into consideration. Figure 9.4e shows temperature distribution for simulation ca se 3. As the effects of the well mixed air flow, the region on the s upply side has lower temperature (less than 22C). The lower part toward the exhaust side of the room also has such low temperature due to the effect of the exha usting flow. Scattered small regi ons of high temperature exist around the lights and bodies. The high temp erature region in the upper part on the exhaust side of the room act ually has moderate temperatur e (23C) as compared to that in simulation case 1.
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164 Relative humidity distribution in Figure 9.4f, again, show s an inverse image of temperature in Figure 9.4e. Humidity is 62% in the well mixed region and around 56% in the still air region occupied the upper part on the exhaust side of the room. For simulation cases studied, 1 and 3, the air flow pattern plays an important role on both thermal comfort and contaminant control. Figure 9.5 shows a comparison of the air flow patterns for the two cases by examin ing their representative streamtubes. For each simulation, the streamtubes originated fr om three starting points numbered from 1 to 3 on the supply opening are plotted. The ends of the streamtubes are numbered respectively. In Figure 9.5a, all these streamtubes go dow n at first due to buoyancy effect as discussed previously, then moves separate ways that represent three types: streamtube 1, started closest to the obstacles, moves ar ound the room follow a co mplex path, loses all of its momentum and dies out inside the room ; streamtube 2 makes a curl before exiting through the exhaust opening and str eamtube 3 exits straightly. In Figure 9.5b, the flow patterns are different. All three streamtubes move straight at first, but it can be observed that as the starting point gett ing farther away from the central region, the streamtubes tend to drop down slightly because of the la ck of supporting vertical flows from the central region. Streamtube 1 absorbs the mome ntum from the vertical flows; move past the lights then goes back to the supply wall an d forms a horizontal circulation close to the wall. It later goes down, move s through the surgical field in a crooked path and exits straightly through the exhaust opening. Stream tube 2 moves in a simple path around the lights then goes down and exits straightly. Streamtube 3 falls st rongly for there is no supporting vertical flow far from the central region, and then dies out without exiting the room.
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165 (a) Simulation case 1 ( YS = 1.5 m, YE = 1.5 m) (b) Simulation case 3 ( YS = 0.5 m, YE = 1.5 m) Figure 9.5 Comparison of air flow patterns from simulations cases 1 and 3
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166 As mentioned previously, the effects of the design factors on a response on thermal comfort or contaminant removal should be modeled in a systematic approach. The design factors in this case are the horiz ontal locations of th e supply and exhaust grilles ( YS and YE). The responses of interest are mean (in BZ) contaminant concentration, CRE, PMV for the patient and the staff memb er 1. The first two responses are for contaminant removal and the last four are for thermal comfort. The values of these responses for 9 simulation cases are readily computed. How th ey are related to the design factor YS and YE is presented in Figure 9.6 to Figure 9.11 where each one presents three different curved surfaces by their contour plots explained as follows: Part (a): a response surface is built from 9 data corresponding to 3 values of YS and 3 values of YE by using the twodimensional spline interpolation. Part (b): Generalized Linear Model (G LM) with Analysis of Variance (ANOVA) test is used. Details on GLM and ANOVA can be found in Searle (1971) or McCullagh and Nelder (1999). The starting GLM has the form: 2 E 5 2 S 4 E S 3 E 2 S 1 0Y K Y K Y Y K Y K Y K K Z (9.24) The response Z can be the mean contaminant concentration, CRE, or PMV for the patient or staff member 1. After fitting the 9 data into the GLM, Analysis of Variance (ANOVA) is used to test for significance of the terms in the model by using statistical significance (pvalue). The terms that have pvalue > 0.05 are dropped out of the model and another ANOVA is used to test for signi ficance for the new model. The results show that all final 9 models fo r 9 responses involve only YS and YS terms; all models have pvalue < 0.005 (99.5% reliable). A check usi ng the normal probability plot for a graphical normality testing of residual (the difference between the predicted values from model and
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167 the observed values from simulations) shows that the normality assumption is reasonably satisfied. The contour plots show ver tical lines due to the absence of YE from the models. Part (c): a model based on only 4 data points from the first 4 simulations which forms a twolevel experimental design w ith two factors. The model has the form: E S 3 E 2 S 1 0Y Y K Y K Y K K Z (9.25) Since all the correlations of the respon ses to the design factors are nonlinear by nature, the pure linear model Z = K0 + K1YS + K2YE can never significantly fit. The interaction term K3YSYE is used to loosely replace the nonlinear effects. There are already 4 unknown coefficients to find ( K0, K1, K2, and K3) in this GLM, leaving no data for any ANOVA test for significance. This model is th e same as the result from twodimensional spline interpolation for 4 data on 2 values fo r each factor. A comparison of this simplest model and the more complex model can help drawing some conclusions which will be useful when there are many design factors to consider such that more than twolevel experimental design is no longer proper. Figure 9.6 shows the correlation for mean contaminant concentration, the GLM becomes linear and shows good agreement with interpolation (9 data ) with the minimum response corresponding to YS = 0.5 m. Interpolation (4 da ta) gives minimized response at YS = 0.5 m and YE = 1.5 m, showing insignificant effect of YE into the model. Therefore, to minimize the mean contaminant concentra tion in the operating room, a designer should consider placing the supply grilles closer to the centerline, while the exhaust grille locations do not make a ny significant difference. Figure 9.7 shows the correlation for CRE which needs to be maximized. The GLM is quadratic to YS, barely conforms the interpolat ion (9 data). Both give the
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168 maximized response respect to YS = 0.6.8 m. The interpolati on (4 data) cannot describe the quadratic relationship and gives the maximum at YS = 0.5 m and YE = 1.5 m. Thus, in order to gain the maximum CRE, th e intake location has to be around YS = 0.7 m. Figure 9.8 shows the correlation of PMV for the patient. The GLM is quadratic and in good agreement to the interpolat ion (9 data) giving the minimum at YS = 0.8.9 m. The interpolation (4 data) cannot descri be the quadratic rela tionship and gives the minimum at YS = 0.5 m and YE = 1.5 m. Therefore, the most comfortable condition for the patient can be achieved by moving the supply grilles away from th e central location to around YS = 0.85 m. This is not surprising in an operating room since avoiding direct impingement of cold air while the patient does not have adequate insulated clothing will make him/her more comfortable. However, this action will result in higher level of mean contaminant concentration (Figure 9.6) which is not desira ble. A possible solution can be to design for lower contaminant concentrati on while providing the patient with more thermally insulated clothing. Figure 9.9 shows the correlation of PMV for the staff member 1. The GLM is linear and in reasonably good agreement to the interpolation (9 data) and very good agreement to the interpolation (4 data). All give the minimum at YS = 0.5 m. Figure 9.10 and Figure 9.11 show the correlations of PMV fo r the staff members 2 and 3. They are very similar. The GLM is quadratic and in good agreement to the interpolation (9 data) giving the minimum at YS = 0.5 or 1.5 m. The interpol ation (4 data) although cannot describe the quadratic relationship but still gives one agreeable minimum at YS = 0.5 m. This suggests that moving the supply grilles cl oser to the center will provide higher level of comfort for all staff members.
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169 (a) Interpolation (9 data) (b) GLM/ANOVA (9 data) (c) Interpolation (4 data) Figure 9.6 Mean contaminant concentration as function of YS and YE (a) Interpolation (9 data) (b) GLM/ANOVA (9 data) (c) Interpolation (4 data) Figure 9.7 CRE as function of YS and YE
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170 (a) Interpolation (9 data) (b) GLM/ANOVA (9 data) (c) Interpolation (4 data) Figure 9.8 PMV for patient as function of YS and YE (a) Interpolation (9 data) (b) GLM/ANOVA (9 data) (c) Interpolation (4 data) Figure 9.9 PMV for staff member 1 as function of YS and YE
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171 (a) Interpolation (9 data) (b) GLM/ANOVA (9 data) (c) Interpolation (4 data) Figure 9.10 PMV for staff member 2 as function of YS and YE (a) Interpolation (9 data) (b) GLM/ANOVA (9 data) (c) Interpolation (4 data) Figure 9.11 PMV for staff member 3 as function of YS and YE
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172 9.4 Conclusions This chapter presents a thorough analysis of air velocity, pressure, temperature, humidity distributions, and contaminant tran sport in an airconditioned hospital operating room using a 3D computational model. Huma n thermal comfort using simple assessment and PMV model as well as contaminant remova l effectiveness are studi ed. It is found that air flow pattern significantly affects the performance on both contaminant removal and thermal comfort. For simple assessment on thermal comfort, the mean air speed and mean relative humidity can be taken over the en tire space or only over the breathing zone without much difference. However, mean te mperature can be varied significantly over different air zones. It is best to take mean temperature ove r occupied zone or breathing zone since the condition is closer to the occupants. Simple assessment based on mean temperature shows that the horiz ontal location of the supply gr illes has significant effects of thermal comfort while that of the exhaus t grilles does not. The GLM approach for the PMV and contaminant concentration distributi on characteristics conf irms strong effects of the horizontal location of the supply gr illes on thermal comfort and on contaminant removal. A comparison between different res ponse models shows that GLM can be used to replace the interpolation for threelevel experimental design in most cases and that the interpolation for twolevel experimental da ta shows reasonably good agreement to other models when there are almost only linear eff ects. For overall design of the room, it can be concluded that the closer th e supply grilles to the cente r of the room, the better the performance is on both contaminant removal and thermal comfort.
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173 Chapter 10 A Guideline on Using CFD for Indoor Space Modeling 10.1 Introduction The use of computational fluid dynamics (CFD) tools in indoor environment design has been increasing in recent year s. Although modeling so ftware is widely available, successful applic ation of CFD method in indoor environmental modeling is still challenging (ASHRAE, 2005). CFD modeling and simulation for indoor spaces require fundamental and advanced backgrounds in fluid mechanics and heat and mass transfer as well as computational expertis e. In some cases, CFD approach is not applicable because of time and computing re sources required become impractical due to a large number of elements in the computationa l mesh. The American Society of Heating, Refrigerating and AirConditioning Engineers (ASHRAE) recently announced a request for proposal on optimizing the trade off between grid resolution and simulation accuracy (ASHRAE, 2007). The most updated ve rsion of the Fundamentals Handbook by ASHRAE (2005) provides an introductory f undamental guideline on the CFD method for indoor environmental modeli ng. It gives an overvie w to CFD method for HVAC engineers who attempt to use CFD modeling fo r their works. A more complete guideline is necessary to provide the HVAC engineers a systematic a nd effective procedure to set up a CFD model and run simulations on it. Based on the work presented in Chapters 7, 8, and 9, this author proposes a guideline on several practical aspects related to the application of CFD in indoor
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174 environmental modeling, as a complementary part to the general guideline given in the Fundamentals Handbook by ASHRAE (2005).Thi s guideline was developed with a practical point of view for HVAC engineers. Only a basic set up for modeling and simulation is presented with brief notes on advanced considerations. Although the commercial packages FIDAP (Fluent, 2005) fo r both creating and meshing the geometry and simulation, and GAMBIT (Fluent, 2006) for creating and meshing the geometry only, especially useful for handling complex geometries, were employed for demonstration purposes, the methodology can be applied with any CFD/mesh generation software provided that they have basic features for a CFD task. Most indoor spaces are 3D by nature, that is, all three dimensions have their own complexity in both geometry and physics. Th erefore, using 3D models to describe indoor spaces is the most natural and reasona ble choice. For a highly 3D space, which is usually the case, the use of 2D models may lead to unrealistic solutions. However, the use of 2D models has its own advantages and needs to take into consideration. In some cases where the complexity in one directi on is simpler than th at in the other two directions, a 2D model can be used to a pproximate a 3D space of interest and gives good results. Although a 2D model cannot desc ribe the transport phenomena accurately, 2D modeling and simulation can provide usef ul information and id eas to 3D modeling and simulation while taking less time, computi ng resources, and working efforts. Useful information and ideas may include the set up of the model, the order or range of the solution, even some insightful of the physic s of the problem, etc. Therefore, it is recommended that simplified 2D modeling a nd simulation should be performed before one proceeds to work on more realistic 3D modeling and simulation. In most cases,
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175 creating the geometry and meshing of a 2D model can be extended to that of a 3D model for the same physical problem. A 2D model can also be used to test if a mathematical model (governing equations and boundary conditions) as well as its associated numerical values ( physical properties, prescribed boundary quantities, etc.) are set up properly before applying for a time consuming 3D simulation. The basic steps in CFD modeling and si mulation (adapted from ASHRAE, 2005) are as follows: Creating the geometry and meshing Specifying physics settings Solving the model Postprocessing and visualization The following subsections present the technical aspects of these steps. 10.2 Creating the Geometry and Meshing The first step in developing a computati onal model is creating the geometry and meshing. A real physical problem is usually complicated in many aspects including its geometry. Sometimes, a space of interest has no clear boundaries so that imaginary sides and hypothetical boundary conditions have to be made up to isolate the space of interest from the surroundings to form a geometry that can be modeled. Fortunately, most indoor spaces such as rooms are closed spaces confined by solid sides (walls, closed doors, etc.). Therefore, it is a natural appro ach to model the geometry of an indoor space as it is, with reasonable simplifications. Once a space of intere st is determined, further considerations are required to try to reduce the size of the computational domain. The symmetry of both geometry and boundary conditions are often used for this pur pose: it is possible to model
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176 only a half or a quarter of the space of interest if it has one or two pe rpendicular planes of symmetry. This type of symmetry considera tion can be found in the problems presented in Chapter 5 (3D model of stor age tank for liquid hydrogen) and Chapter 9 (3D model of operating room). Another type of symmetry consideration is for the long and repetitive spaces, such as the corridor or the hallway. In such cases, a volume section can represent the entire space by repeating itself and put th em sequentially. This type of symmetry can be found in the problem presented in Chapter 7 (3D model of re frigerated warehouse). It is important to make sure that the symmetry is satisfied not only for the geometry but also for the boundary conditions. The resize of a geom etry model from the whole to a fraction of the space of interest can significantly he lp saving time and computing resources for modeling and simulation, especially for 3D problems. Meshing is the process of discretizing the geometry that models the physical domain of interest into a large number of elements. The accuracy and costeffectiveness of the numerical solution for the modeled physical problem is highly dependent on the mesh. This task is tedious, difficult and timec onsuming. It may take the major part in the datapreparation stage of an analysis which can consume up to 80% or more of the laborhours required (FIDAP Documentation, Fl uent, 2005). Therefore, a methodology that allows the development of an effectiv e approach to meshing is necessary. A computational mesh is composed of many small elements. In CFD and computational mechanics in general, there ar e a few simple shapes of element widely used: triangles and quadrilatera ls for 2D problems, tetrah edrons (4sided triangularbased shapes) and hexahedrons (6sided box shapes) for 3D problems. There are also wedges (triangular prisms) and rectangularbased pyramids so metimes used to transition
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177 in hybrid 3D mesh. A mesh of elements can be classified as struct ured (that is, having consistent geometry regularity and families of grid lines in one direction do not cross each other, ASHRAE, 2005) or unstructured. This guideline pr esents an approach to the development of specifically structured quadril ateral for 2D and hexahedral meshes and 3D problems. Most indoor spaces are box shapes. Therefor e, a meshing strategy that aims to fill the space of interest with boxshaped elements (rectangular pa rallelepipeds or cuboids) is natural. However, two issues need to be ta ken into account for a fl uid flow and heat and mass transfer problem. First, layers of struct ured and fine enough me sh are needed on all fluidsolid interfaces, such as the walls, the ceiling, and the floor of the indoor space and the surfaces of the object s within the space such as people, furniture, equipments, etc., to capture possibly high gradients of the transport phenomena th ere. Second, the presence of the mentioned objects disrupts the box shape of the space. This makes it much difficult to generate a mesh, unlike meshing of an empty sp ace. In the case that these objects can be modeled as box shapes that have the same pr incipal directions as the whole space, the space can be divided into many boxshaped subvolumes accommodating the (rectangular) surfaces of the objects. Each subvolume then can be meshed with structured boxshaped elements as straight forward as meshing a boxshaped empty space. This method is intuitively na tural and is a common practi ce for meshing such boxlike spaces (or similarly rectangularlike spaces in 2D problems). One disadvantage of this approach is that the fine mesh attached on a surface of an object (t hat represents a fluidsolid interface) usually extends into the mesh of the adjacent subvolumes (that models a part of the bulk fluid) where such fine mesh is not required. This leads to an unnecessary
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178 increase in the number of elements in the mesh. For some cases, the objects may have complex geometries of great importance, which cannot be approximated as box shapes. In such case, the boxshapedelement mesh is very difficult to generate without an effective strategy. The meshing approach presented in this gui deline is based on the encapsulation of the regions that require special meshing trea tments such as the complex geometries and fluidsolid interfaces. The main global space excluding these local regions is subdivided further if necessary and mesh ed with high quality regular elements (squares or cubes). The subdivision of the local regions and the gl obal space are set up su ch that their mesh generation can be automated conveniently us ing only basic meshing schemes available for most mesh generation software. Examples on modeling of a hospital operating room (Chapter 9) are presented to demonstr ate the underlying methodology. The mesh development for the 2D model is introduced fi rst for its simplicity. Then that meshing approach is extended to the mesh development for the 3D model. 10.2.1 Mesh Development for 2D Model Figure 10.1 shows the mesh generated for the 2D model of the hospital operating room presented in Chapter 9. The rectangular objects within the space numbered 1 to 4 represent the light, the lying patient, and the standing staff. Their areas are excluded from the computational domain and their sides are fl uidsolid interfaces. Th e four sides of the rectangle that bound the computational domain represent the walls, the ceiling, and the floor of the room and they are fluidsolid in terfaces. Those fluidsolid interfaces are the regions that require special meshing treatm ents. The two line segments on the two walls represent the inlet and outlet openings. They also need special meshing treatments for the
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179 accommodation of finer mesh next to the solid ed ge shared with the wall, and of adequate number of elements on these short line segmen ts without propagating the fine mesh to the adjacent space unnecessarily. The global space is planned to have a squareelement mesh. Among the types of quadrilateral elements, s quare elements possess the perfect quality: zero skewness and unity aspect rati o. The side of the square el ement is selected to be the nominal size of the mesh Each object of interest is created in a local coordinate system. The objects can be moved from place to place by redefining the positi on of the origin of the local coordinate system to suit the needs of the simulation task. This is especially useful for a parametric study involving geometric positions. Figure 10.1a shows the object s of interest with their associated local coordinate systems. Encapsulation: the objects 14 are enclosed by sli ghtly larger auxiliary rectangles as shown in Figure 10.1a. Each side of these auxiliary rectangles is calcul ated such that it is a natural number multiplied by the nominal size The band created by the difference between an auxiliary rectangl e and the corresponding rectangul ar object is divided by four line segments, inclined at 45 degr ees, into 4 trapezoids as shown in Figure 10.1a. These trapezoids can be meshed simply as shown in Figure 10.1b. It can be observed in Figure 10.1b that in each trapezoid the number of elements in one dire ction is dictated by the nominal mesh size while in the other direction the height of the element layers from a fluidsolid interface increases inwa rd the global space by a growth ratio Knowing the height of a trapezoid the number of elements and the growth ratio in this direction can be calculated to ensure th at the layers of elements at these boundaries are thin enough to be able to capture the possibly high grad ients of solution there while not producing too
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180 large aspect ratio, which may affect the computation accuracy. It can be observed that if the inside of the rectangular objects are included as part of the computational domain, it can be meshed easily without changing the mesh in the global space. The fluidsolid interfaces along the external boundaries of the space are treat ed similarly as shown in Figure 10.1a and partly in Figure 10.1c, except for the regi ons around the inlet and outlet openings that required further treatments. Figure 10.1c shows the expanded view of the region around the inlet opening. The encapsulation technique is used to control the mesh inside the local region around the inlet openi ng while ensuring that the outer border of this local region is matching to the nominal mesh size in the global space. As the results of the encapsulation, th e global space has a ll its sides being a natural number of th e nominal mesh size and perpendicular to each other at shared vertices. This shape allows the global space to be able to accommodate a mesh of only square elements of nominal size Due to its complexity, the global space can be divided into several simpler shapes (in the sense that the particular softwa re used by user can mesh automatically if the nominal size is given) as shown in Figure 10.1a. In the case where more advanced meshing options are not available, the global space can always be divided into many rectangular subregions that can accommodate nominal size squareelement meshes. The option of meshing such re ctangles automatically is standard to any mesh generation software or module in a CFD package. For the mesh presented in Figure 10.1, the following numerical values for the mesh parameters are used: = 0.1 m, = 0.05 m, = 3 and = 1.5. The result mesh has 1496 square elements in total 2570 quadrilateral elem ents (that is, 58% of the number of elements is of perfect quality).
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181 (a) Full view (b) Expanded view: corners of objects (c) Expanded view: inlet opening 1 2 3 4 1 2 3 Figure 10.1 Geometry decomposition and meshing for 2D model
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182 10.2.2 Mesh Development for 3D Model Figure 10.2 presents the geometry and its decomposition of the 3D model for the study on an operating room (pr oblem description is in Chapter 9). Figure 10.2a shows the geometry model of a half of the room due to its mirror symmetry. The objects within the operating room space (the light, the lying patient, and the standing surgical staff of three) are modeled as box shapes and created in their local coordinate systems. Encapsulation: auxiliary box shapes are created to enclose the boxshaped objects Figure 10.2a. These auxiliary box shapes are of slightly larg er size than the objects. The outer surfaces of these box shapes are chosen such that each plane side can accommodate a regular mesh of square elements of nominal size The transition volume created by the difference between an auxiliary box sh apes and the corresponding boxshaped object is decomposed into several rectangular base d prismoids (hexahedrons with two parallel rectangular bases and four side s of either trapezoid s or parallelograms) by cutting planes inclined at 45 degrees to principal planes. The external boundaries (ceiling, floor, and three walls) are treated similarly with the auxiliary box sh apes slightly sm aller than the box shape of the entire volume. The correspond ing transition volume is also decomposed into several rectangular base d prismoids. The inlet and out let openings are rectangles on two opposite walls and needs to be treated spec ially in order to pres erve the 2D squareelement mesh on these two walls as well as the 3D cubicalelement mesh in the global space volume that the approach intends to generate. In 2D model (Figure 10.1), the inlet and outlet openings are line segments and can be meshed easily as parts of the walls without having their own transition zones. Th e transition zones have the sole purpose of increasing the number of elements on these opening segments. However, in 3D case, a
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183 transition zone is needed for preserving th e regular mesh nearby. For an opening, two auxiliary box shapes are needed: one has th e opening area as a base like a boxshaped object, and the other one is sl ightly larger to enclose the former. The decomposition of the transition volume is similar to that in the other transiti on zone around the objects. The global space excluding these auxiliary box shapes needs further volume decomposition to make it easier to mesh using basic meshing schemes. Figure 10.2b shows the result of the decomposition with the component volumes di sassembled. The transition subvolumes are kept together to show their connectivity. Figure 10.3 shows the hexahedralelement mesh using encap sulation technique. The color represents the skewness quality of the elements. Blue means higher quality (low skewness) and red means lo wer quality (high skewness). In Figure 10.3a, the bulky blue volumes represent the global space meshed with cubical elements, which have zero skewness or perfect quality. Figure 10.3b shows the expanded views of the important transition zones around the inlet and outlet openings and the su rgical site where locates the objects within the space. It gives an illu stration of how different transition zones are meshed with the same approach and how thei r outer surfaces are de veloped to interface the cubicalelement mesh in the global space. Figure 10.4 presents the hexahedralelement mesh for the entire volume of the 3D model as a combination of the layered refi ned element mesh in the transition zones at boundaries and the cubicalelement mesh that occupies the global sp ace. For controlling the mesh size, the same parameters as in 2D case can be used. The mesh in Figure 10.4 used = 0.1 m, = 0.05 m, = 3 and = 1.5. It has 35140 cubi cal elements in total 56290 hexahedral elements (that is, 62% num ber of elements of perfect quality).
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184 (a) Full view (b) Subvolumes from geometry decomposition Figure 10.2 Geometry decomposition for 3D model using encapsulation technique
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185 (a) Full view (b) Expanded local views (from left to right): inlet (supply), surgical site, outlet (exhaust) Figure 10.3 Hexahedral mesh for 3D model using encapsulation technique
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186 (a) Layered hexahedralelement mesh on fluidsolid interfaces (b) Cubicalelement mesh in bulk fluid space Figure 10.4 Refined mesh in transitio n zones and regular mesh in global space
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187 10.3 Specifying Physics Settings 10.3.1 Governing Equations a nd Physical Properties In a many CFD packages commercially av ailable, the governing equations and its formulation for a numerical me thod are predefined and the us er only need to enter the relevant physical properties to the CFD software. Howeve r, since generalpurpose CFD software may have many features beyond the n eeds of the user for a particular problem, he or she will have to specify which equatio ns is necessary. For typical HVAC&R indoor spaces, the fluid of interest is air. Air borne species such as water vapor and contaminant gas (odor, carbon monoxide, etc.) is often of in terest also. The air, as a carrier fluid in case there are some other species, is usually considered incompressible. To solve for the airflow, the continuity equation and the mo mentum equations (NavierStokes equations) are needed. The buoyancy effect is always significant in HVAC&R sp aces; therefore, the buoyancy term should be included in the momentum equations. Since the buoyancy term introduces temperature into the momentum e quation, the energy equa tion is also needed. In cases there are species of interest, the sp ecies transport equations are needed as well. For air mixture as an incomp ressible fluid, the governing equations for fluid flow and heat and mass transfer in an indoor space can be written as follows: 0 u (10.1) refT T p t g u u u u uT (10.2) T k T t T cp u (10.3) k k k kD t u (10.4)
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188 The governing equations show that the re levant physical prop erties are density dynamic viscosity specific heat cp, thermal conductivity k volumetric coefficient of thermal expansion and species diffusivity Dk. These are the input needed for a CFD simulation. Although the fluid (air) pr operties are often temperature dependent, and the governing equations in most CFD software can include th at effect, indoor spaces are usually have a short range of te mperature, in the order of a few degrees Celsius, in most part of the space, the constant properties assumption is reasonable. Therefore, it is advisable to use constant air properties for a basic set up of a CFD simulation. 10.3.2 Turbulence Modeling Airflow in built environments is predominantly turbulent (ASHRAE, 2005). There are several approaches for modeling turbulent flows, such as ReynoldsAveraged NavierStokes (RANS), large eddy simulation (LES), and direct numerical simulation (DNS). However, although LES and DNS a pproaches have promising developments, their applications in indoor spaces are still limite d due to computing resources required. RANS approaches are widely employed in modeling indoor spaces. There are several turbulence models to us e with a RANS approach. The most intuitive approach is to adopt the mixing length hypotheses (ASHRAE, 2005). The mixing length turbulence model is also known as the zeroequation model, sin ce it does not introduce any new partial differential equation into th e system of governing equatio ns. Other turbulence models may introduce one or two extra partial differe ntial equations, thus increase the computing time and memory required significantly. Theref ore, it is advisable to use the mixing length turbulence model for a basic set up of a CFD simulation.
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189 10.3.3 Boundary Conditions A typical indoor space usually has solid wall s and inlet and outlet openings. It is required to input boundary conditions for velocity temperature, and species, if any. The following guidelines are for a basic set up of a CFD simulation. On the inlet openings: constant prescrib ed velocity, temperature, and species concentration(s): 0 0 0, ,k kT T V u (10.5) On any fluidsolid interface, velocity is zero: 0 u (10.6) On any fluidsolid interface where no mass transfer occurs, the species insulated condition can be used: 0 nk (10.7) On any fluidsolid interface where no heat or mass transfer occurs, the thermal insulated condition can be used: 0 n T (10.8) On the external boundaries of the computa tional domain, that is the fluidsolid interfaces at the solid walls of an indoor space, there are two typi cal cases. The thermal insulated condition (10.8) can be used if the indoor space has negligible exposure to outdoor environment, such as a room in the middle of a building. If the indoor space has significant exposure to outdoor environment, su ch as the case of refrigerated warehouses, the linear heat transfer model can be used:
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190 0T T h n T k (10.9) On the fluidsolid interfaces at the bounda ries of the objects within the indoor space, typical cases for temperature boundary conditions are prescribed temperature (human body) and prescribed heat flux (light computers, equipments, human body, etc.): 0T T (10.10) 0q n T k (10.11) On the fluidsolid interfaces at the bounda ries of the objects within the indoor space, a typical case for species bounda ry conditions is species mass flux: 0 ,k k kq n D (10.12) 10.4 Solving the Model After two previous steps (the creating ge ometry and meshing, and the specifying physical properties and boundary conditions), the computational model is complete. This computational model is submitted to a solver module in a CFD package. The computing of the numerical solution for a CFD problem ta ken place in this step is quite transparent to the user. CFD software such as FIDAP allo ws the user to monitor the convergence rate of the computation. It is a good idea to check convergence rate from time to time to see if the simulation is converging as expected. After a simulation is done, the solution need s to be check in several ways. Simple postprocessing commands available in most CFD software can be used to visualize the airflow and temperature distri bution to see if the phenomen a are reasonable for a quality check. The macroscopic heat and mass balance (thermodynamics) can be used to check
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191 the solution quantitatively. Check ing the range of the solution is also useful for ruling out solution containing unrealistic numbers. For a grid independence study, the size of the mesh is changed systematically and simulations with different me shing size are submitted again. The novel meshing approach presented in the previous s ubsection allows the control of the mesh size through four parameters, which can be changed conveniently to generate a new mesh of different mesh size. After several runs for different meshes, representative values of a solution such as average speed or temperature can be plotted versus the mesh size to decide the proper mesh size where the solution shows mesh i ndependence as the mesh size decreases. Once a good solution obtained, several modifi cations to the model can be applied. Temperature dependent properties, different turbulence models, and more complex and realistic boundary conditions can be tried. This step involves many tasks to ensure the completeness and accuracy of the CFD simulation. There are also extensive disc ussions on these issues and others in the Handbook by ASHRAE (2005). 10.5 Postprocessing and Visualization Most CFD software has its own postpro cessing module including solution graphic visualization. For a quantitative assessment a fluid flow and heat and mass transfer, the values of average and maximum and spatial stan dard deviation of a variable such as fluid temperature or speed are often used. The visualization of a nume rical solution such as the airflow or the temperature distribution is important to examine and understand the transport phenomena. Based on the understanding of the phenomena in an exis ting simulation, design decisions can be
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192 made and checked by using another simulati on that implements the modified design ideas. For a CFD simulation, the visualiza tion of any variable can help the overall understanding of a complex pr oblem. Each variable need s a proper presentation for revealing its distributi on structure as recommended in the followings: Velocity: streamline plot combined with a slice plot for fluid speed Pressure: isosurface plot Temperature: slice plot or isosurface plot Species concentration: slice plot Appendix I: provide MATLAB c odes for 3D visualization for the solution of the problem on the hospital operating room (Chapter 9). The resulti ng plots can be found in Chapter 9. These MATLAB codes can be modified to suit other 3D problems.
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193 Chapter 11 Conclusions 11.1 Numerical Modeling and Simulati on of Heat and Mass Transfer Seven problems involving heat and mass tran sfer in cryogenic liquid storage and HVAC&R applications have been studied and presented. Liquid hydrogen and air are the incompressible fluids considered in thes e problems. CFD modeli ng and simulation has proved to be a powerful tool for the investig ation of heat and mass transfer phenomena in detail at microscopic (continuum) level for th ese fluid systems. Th e numerical solutions from the CFD simulations give the values of the primary transport variables such as velocity, pressure, temperature, and species concentrations at ev ery nodal points over the entire computational domain that describes the space of interest. The distributions of secondary variables such as relative hu midity and predicted mean vote (PMV) for thermal comfort assessment can be computed based on the distributions of the primary variables. The distributions of these variables can be graphi cally visualized in properly selected plots that can give more insightful understanding of the inside structures of these distributions thus the underl ying transport phenomena. The vi sualization of a numerical solution combined with a parametric study can show how the fluid flow and heat and mass transfer change within the space of inte rest as one or many geometric parameters or boundary conditions change. On an engineering point of view, this knowledge is critical for both improving an existing system and de signing a new system. In many cases where a single value is used to assess a system on a particular aspect, the average or maximum
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194 value of a transport variable such as temperature, velocity, etc., can be employed. To assess the uniformity of a transport variable, the spatial standard deviation is a natural choice. These single values are the characte ristics of a distribut ion and can be easily extracted from the numerical solution of the transport variable of interest. Four designs of ZBO storage tanks fo r liquid hydrogen has been proposed and investigated on the effects of the design parameters to the performance of the tanks, especially the antiboilingo ff characteristics represented by the maximum temperature within the fluid and the pres ence of high temperature regi ons where the hot spot of maximum temperature may be located. Geom etric dimensions, forced flow velocity, cooling cycle, and other desi gn parameters have been planned in parametric studies through steady state and transient analysis. For the first storage tank design where the fl uid is cooled outside and is injected into the bulk fluid of the tank through nozzles on a nozzle head, the increase of flow rate yields the decrease of maximu m temperature. The increase of supply flow rate obviously requires more power consumption and thus incr eases the cost of maintaining the system operation. Among the geometric parameters unde r study, the depth of the nozzle head has quite significant effect on maximum temper ature and needs to be designated around the middle of the height of the tank for lower maximum temperature. For the second design that has a large num ber of lateral pumpnozzle units placed around a heat pipe, the results show that a smaller gap between the nozzle and the heat pipe yields better performance: lower maximu m temperature, lower average temperature, and more uniform temperature distribution in the fluid. Other geometric parameters also have some less significant effects on the c ooling performance of th e system. The use of
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195 an axisymmetric model for this problem saves time in modeling and simulation due to the reduction of the number of space dimensions as well as the number of elements compared to that of a 3D model. However, this simp lification may have its limitations, especially for not being able to describe accurately the fl uid flow and heat transfer within the tank. The axisymmetric model assumes an infinite number of pumpnozzle units distributed around the heat pipe that form a solid body that blocks the flow from a nozzle to reach the opposite surface of the tank wa ll. In an actual system w ith a finite number of pumpnozzle units, there are gaps be tween two adjacent units that allow the fluid discharged from a nozzle head to flow quite freely to th e opposite region of the fluid within the tank after being in contact with and wrapping around the side of the heat pipe. Such flows cannot be described in an axis ymmetric model. If they ar e important to the transport phenomena in the tank, the use of an axisym metric model may cause unrealistic results. The simulation using the 3D model with a heat pipe and a single lateral pumpnozzle unit gives a detailed description of the distributions of velocity and temperature. It shows that the fluid flow going around the heat pi pe is a major part of the total flow from a nozzle head and plays an important role in reducing the temperatur e in the fluid body. Both the axisymmetric model (infinite numbe r of pumpnozzle units) and the 3D model (single pumpnozzle unit) show an agreement that the maximum temperature in the fluid decreases as the fluid velocity (thus the flow rate) discharged from the nozzle increases. However, the observation that the maximum te mperature for the axisymmetric model is higher than that for the 3D model may possibl y be unrealistic due to the limitation of the axisymmetric model. A future work on 3D m odeling of a storage tank with heat pipe and a finite number of pumpnozzle units can be performed to explore this matter further.
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196 The transient analysis for the last desi gn of ZBO cryogenic storage tank for liquid hydrogen with a heat pipe and an axial pumpnozzle unit shows that the cooling scheme under study can work for only about 2 weeks. Th is cooling scheme was planned that the pump switched on at a temperature threshold of 23 K, ran for 1 hour then stopped, then switched on when the maximum temperature r eaches the threshold again. The detailed study on each stage of the proposed operati on cycle provides useful ideas to the development of improved operation cycles for longerterm storage. For the refrigerated warehouse, cooling e ffectiveness and temperature uniformity are of most importance. The location of the cooling unit has been st udied systematically resulting in applicable guidelines for findi ng an optimized location based on the design criteria that takes priority (maximum temp erature, mean temperature, or temperature uniformity). The results show that the maxi mum temperature, the average temperature, and the spatial standard deviation of temp erature distribution te nd to decrease as the cooling unit moves closer the st ored packages in the followi ng directions, respectively: horizontal, vertical, and bot h horizontal and vertical. A compromised design can be selected where the cooling unit is located hi gher and in front of an array of stored packages, as close as possible to the top of the first stack. This location of the cooling unit is also required to follow another set of guidelines on warehous e operation, that is, minimum safety distance from the cooling unit to the stacks for loading and unloading activities. These guidelines are useful for the design of a re frigerated warehouse. For an existing warehouse, these guideline s can also be used to deci de the height of the stacks and the location of the first stack.
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197 For the problems involving indoor spaces, thermal comfort is of great importance. The use of the PMVPPD model can be used for assessing thermal comfort in an HVAC space conveniently. In the modeling phase, it is better to generate a subdomain "body" wrapping around each occupant. This approach can serve two purposes. The first one is that the values of the parameters relevant to the computing of the PMVPPD model can be taken closer to the body of the occupant and reflect better his or her comfort condition. The second one is that the mesh density in side this "body" subdo main can be closely controlled while the outer surfaces match the si ze of the regular element in the vast space outside. The PMV calculated based on th e small space around the person is obviously more accurate than the PMV calculated based on the entire indoor space. The former can be higher than the latter a significant amount of about 0.5 on the ASHRAE thermal sensation scale (full scale from 3 to 3). Th is suggests that when an indoor space is analyzed for predicting its occupants' th ermal comfort using CFD modeling, it is recommended that the PMV or other thermal sensation index be cal culated based on the data acquired for the small spaces that enclose the model of the occupants rather than for the entire space. For the study on the hospital operating room, thermal comfort is also considered, but contaminant removal effectiveness of the ventilation systems is of most importance. The locations of the supply and exhaust openings play a critical role in controlling these characteristics of the system. The GLM approa ch was adopted to analyze the effects of the design parameters. This study has demonstrated the use of GLM to model the response of the system to the design parameters such as the horizontal locations of the
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198 supply and exhaust openings. This approach can be used for the other design parameters as well. A guideline for the use of CFD method in indoor environmental modeling is presented in Chapter 10. A novel meshing approach based on the encapsulation technique is proposed give a systematic methodology for the meshing of indoor spaces and others in general. Technical aspects on other steps in CFD modeling ar e also presented, giving new CFD users, especially in HVAC&R, practical instructions to ba sic set up and run CFD simulations. The sizes of the models for the proble ms under study are on the order of meters: liquid hydrogen tank (3 m diameter 2.6 m he ight), refrigerated warehouse (7 m length 4 m height 2 m width) residential room (3.7 m length 2.7 m height), operating room (6.1 m length 3 m height 2.15 m width). For the modeling of computational domains of this size, one of the difficulties is that the required computing resources (memory size, machine time, etc.) may exceed the capabilities of the available facilities. The modeling and simulation of the problems under study show s that the use of quadrilateralelement mesh for 2D and axisymmetric models and hexahedralelement mesh for 3D models with mesh density control along fluidsolid interfaces and at complex geometry boundary is effective. This approach gives good accu racy, fast convergence and less computing resources compared with the use of triangular elements in 2D (or axisymmetric) and tetrahedral elements in 3D. Through the prob lems under study, the practical approach for the quadrilateralelement and hexahedralele ment mesh generation with applicable element size and arrangement has been demonstrated. This approach and its demonstrations provide a meshing strategy th at helps the effective utilization of the
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199 available features of any part icular software that an user is working with to accomplish the meshing task. It is also promising to be further generalized and to lead to a fully automatic hexahedral meshing procedure fo r fluid flow and heat and mass transfer modeling problems. If this can be implemented, it will have a great impact on meshing in particular and on CFD modeling in general. 11.2 Future Works All the problems presented in this work have been done as isolated spaces with prescribed boundary conditions to represent the external systems that have been cut off. This helps simplifying the study of the fluid flow and heat transfer phenomena in the space of interest and thus allo ws a thorough analysis in a r easonable time frame. Once the phenomena in an isolated space have been unde rstood, it is necessary to perform further study on the mutual effects of the prescrib ed boundary conditions and the limited energy source that maintains them. A more realistic model can be developed with the inclusion of the external systems for better predicti ons on heat and mass transfer performance as well as more accurate estimation of power c onsumption. The integration of such model into a complete control system loops with si gnal feedback from sensor readings and other control elements and a study on dynamic response can be also useful and feasible. A 3D model for cryogenic liquid storage tank with heat pipe and many pumpnozzle units (2 units due to the finite space of the tank and th e size of a unit) as well as a 3D model for the airconditioned room with ceiling fan are the two problems that need to carry out for more accurate solutions and mo re realistic understand ing of the fluid flow and heat and mass transfer with in the corresponding systems.
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200 The study on the ZBO cryogenic storage tanks can be extended to similar systems for different cryogenic liquid such as liquid oxygen, liquid nitrogen, etc., under different conditions such as on the ground on earth or on th e moon, on orbit or space stations, with other effects such as gravity or asymmetric and periodic heating. The study on the indoor spaces with HVAC&R applications provides fund amental ideas to similar studies such as thermal comfort and contaminant removal in a car or cooling a data cen ter (a facility that houses server/computer systems, teleco mmunications, storage systems, etc.) For 3D modeling, there are commercially available packages of mesh generation that have the options of generating tetrahedralelement meshes automatically. However, a tetrahedralelement mesh usually has a larg e number of elements and therefore requires enormous computing resources in the solvi ng phase. For the same volume and the same element size, a hexahedralelement mesh ha s less number of elements. With less number of elements as well as nodal points, the 3D hexahedralelement me sh saves computation time. A welldeveloped hexahedralelement me sh that reduces the skewness and aspect ratio of the hexahedral elements can also im prove the accuracy of the numerical solution. The disadvantage of the generati on of hexahedralelement mesh is that at this time, even with the aid of software, it can only be pe rformed manually or partly automatically, and thus, very time consuming. Therefore, a hexa hedral meshing strategy is very useful for saving meshing time which usually a major part in preprocessing time. The meshing approach for some 3D probl ems presented in this work (liquid hydrogen tank in Chapter 5, refrigerated warehouse in Chapter 7, operating room in Chapter 9, and further expl anation for a guideline in Chapter 10) can be summarized as follows:
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201 First, any irregular boundary is enclosed in and isolated from the main space by a box shape of slightly larger size such that leaving the large main space capable of being filled by cubical elem ents of a predetermined nominal mesh size. Then in each enclosing box, a few layers of finer elements are assigned a long the boundaries of complex geometry if need ed (such as fluidsolid interfaces). The rest of the enclosing box is filled w ith hexahedral elements (most likely in irregular shapes) such that the oute r surface of the encl osing box match the cubeshaped element mesh in the main space. Based on that meshing approach, the deve lopment of a fully automatically 3D hexahedralelement meshing program can be feasible.
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208 Tressler, D. K., Van Arsdel, W. B., C opley, M. J., Woolri ch W. R. (1968). The Freezing Preservation of Foods AVI Publishing Comp any, Westport, CT. Venkat, S., Sherif, S. A. (2004). Selfpre ssurization and thermal stratification in a liquid hydrogen tank under vary ing gravity conditions, in: Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit pp. 1084410854. White, F. M. (1991). Viscous fluid flow 2nd ed., McGrawHill, New York. Woods, J. E., Brayman, D. T., Rasmussen, R. W., Reynolds, P. E., Montag G.M. (1986). Ventilation requirements in hospital opera ting rooms part I: control of airborne particles, ASHRAE Transactions 92(2), 396426. Woolrich, W. R., Hallowell, E. R. (1970). Cold and Freezer Storage Manual AVI Publishing Compa ny, Westport, CT.
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209 Bibliography Allen, R. J. (1964). Cryogenics Lippincott, Philadelphia. Bailey, C. A., ed. (1971). Advanced cryogenics Plenum, New York. Baker, A. J. (1983) Finite element computa tional fluid mechanics Hemisphere, Washington, D.C. Benjamin G., Jaluria, Y., Mahajan, R. L., Sammakia, B. (1988). Buoyancyinduced flows and transport Hemisphere, Washington, D.C. Bird, R. B., Stewart, W. E ., and Lightfoot, E. N. (2002). Transport phenomena 2nd Ed., Wiley, New York. Eselson, B. N., Blagoi, Yu. P., Grigore v, V. N., Manzhelii, V. G., Mikhailenko, S. A., and Neklyudov, N. P. (1971). Properties of liquid and solid hydrogen Israel Program for Scientific Translations, Jerusalem. Ferziger, J. H., and Peri M. (1996). Computational methods for fluid dynamics SpringerVerlag, New York. Fletcher, C. A. J. (1991). Computational techniques fo r fluid dynamics: volume 1 fundamental and general techniques 2nd ed., SpringerVerlag, New York. Fletcher, C. A. J. (1988). Computational techniques fo r fluid dynamics: volume 2 specific techniques for different flow categories SpringerVerlag, New York. Gresho, P. M., Sani, R. L., and Engelman, M. S. (1998). Incompressible flow and the finite element method: advectiondi ffusion and isothermal laminar flow Wiley, New York. IIR (Internati onal Institute of Refrigeration) (1966). Heat flow below 100K and its technical applications, pro ceedings of the International Institute of Refrigeration Commission I, Grenoble (Pure and Applied Cryogenics, Volume 4), Pergamon Press, Oxford. Majumdar, P. (2005). Computational methods for heat and mass transfer Taylor & Francis, New York.
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210 Mangum, B. W., and Hill, J. E., eds. (1977). NBS Special Publication 491: Thermal analysis human comfort indoor environments Proceedings of a symposium held at the National Bureau of St andards, Gaithersburg, Maryland. McQuiston, F. C., and Parker, J. D. (1994). Heating, ventilating, and air conditioning: analysis and design 4th Ed., Wiley, New York. Sauer, H. J., Jr., Howell, R. H., Coad, W. J. (2001). Principles of heating, ventilating, and air conditioning: a text book with design data based on the 2001 ASHRAE Handbook Fundamentals American Society of H eating, Refrigerating and AirConditioning Engin eers, Atlanta. Vasserman, A. A., Kazavchinskii, Ya Z., and Rabinovich, V. A. (1971). Thermophysical properties of air and air components Israel Program for Scientific Translations, Jerusalem. Versteeg, H. K., and Malalasekera, W. (1995). An introduction to computational fluid dynamics: the finite volume method Wiley, New York. Weil, L. (organizer), (1966). Liquid hydrogen: propert ies, production, and applications (Pure and Applied Cryogenics, Vo lume 5), Pergamon Press, Oxford.
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211 Appendices
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212 Appendix A: FIDAP Subroutine for Computation of Relative Humidity /* Copyright Fluent Inc. All Rights Reserved */ C $Id: fidap_user.F,v 1.24 2002/11/01 20:43:16 devuser Exp $ C C FIDAP User Subroutine Templates C Version 8.7.0 C C Modified by Son Ho, University of South Florida C for computation of relative humidity C based on temperature (T), pressure (P), C and water vapor concentration (SPECIES 1) C SUBROUTINE USRFN (FUNC, XYZ, UF, T, TRB, SPEC, NSPEC, P, DENS, 1 NUMNP, NELEM, NDFCD, NDFVL, IPR, TIME, 2 nxyz, mtpar, conmt, mtprp, nlpar, prop, 3 mxmpar, mxmcon, mxmlab, mxepar, 4 ia, WK, MFIRST, MTOT,IERR,DISP) C #include "IMPLCT.COM" #include "TAPES.COM" #include "NUMBRS.COM" DIMENSION FUNC(NUMNP), prop(*), WK(*), ia(*), dens(numnp) DIMENSION TRB(NUMNP,*), P(NUMNP), UF(NDFVL,NUMNP), T(NUMNP) DIMENSION SPEC(NUMNP,*), XYZ(NUMNP,ndfcd), nxyz(numnp) dimension mtpar(mxmpar,*), conmt(mxmcon,*) dimension mtprp(mxmlab,*), nlpar(mxepar,*) dimension DISP(NUMNP,*) integer indspec(15) data indspec /1,2,3,4,5,6,7,8,9,10,11,12,13,14,15/ C C1 = 5.8002206E3 C2 = 1.3914993 C3 = 4.8640239E2 C4 = 4.1764768E5 C5 = 1.4452093E8 C6 = 6.5459673 DO 100 N=1,NUMNP TK = 273.15 + T(N) PA = 101325. + P(N) S1 = SPEC(N,1) W = S1/(1S1) Pw = PA*W/(0.62198 + W) Pws= EXP(C1/TK +C2 +C3*TK +C4*TK**2 + C5*TK**3 + C6*LOG(TK)) FUNC(N) = Pw/Pws 100 CONTINUE RETURN END
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213 Appendix B: FIDAP Preprocessing Input for Chapter 3 B.1 Geometry and Meshing: FIDAP Commands / FIDAP Input File / GEOMETRY and MESHING / PROJECT: Cryogenic LH2 Tank with Injection Nozzles / Axisymmetric model, SI units / $D: diameter of inlet tube / $H: depth of nozzle head / $L: radius of nozzle head $D = 0.15 $H = 1.3 $L = 1.0 / $Z: multiplication factor for meshes of different element size / $BG: growth rate of element layers at boundary edges / $BL: number of layers of structured mesh at boundary edges / For mesh independence study: $Z = 16, 12, 8, 4, 3, 2, 1.5, 1, 0.75 / For large $Z, if the automatic paved meshing fails, use $BL=1 / For $Z < 1, if the automatic paved meshing fails, omit curve #4 in / section "ADD BOUNDARY EDGE" using a slash (/) $Z = 1 $BG = 1.25 $BL = 3 / $S1, $S2, and $S3: nominal sizes of 3 groups of elements / Set $S1 = 0.1205 for $L = 0.9 or 1.3. / Set $S1 = 0.12 otherwise $S1 = 0.012*$Z $S2 = 0.01*$Z $S3 = 0.004*$Z TITLE LH2 tank w/ displacement cooling nozzle system // FIGEN FIGEN( ELEM = 1, POIN = 1, CURV = 1, SURF = 1, NODE = 0, MEDG = 1, MLOO = 1, MFAC = 1, BEDG = 1, SPAV = 1, MSHE = 1, MSOL = 1, COOR = 1 ) $A = 1.5 $B = 0.65 $C = 1.3 $E = $D/2 $F = $E*SQRT(2) $K = SQRT($A^2$F^2)*$B/$A $G = 0.05 $M = 0.01 $N = 0.02 $P = 0.02 $Q = ($L$M$N$P)/2
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Appendix B (Continued) 214// DEFINE COORDINATE SYSTEMS COORDINATE( ADD, ROTATION, SYSTEM = 2 ) $B 0 0 2 180 COORDINATE( ADD, ROTATION, SYSTEM = 3 ) ($B+$C) 0 0 COORDINATE( ADD, ROTATION, SYSTEM = 4 ) ($H+$B$K) 0 0 2 180 // ADD POINTS / 18: tank wall COORDINATE( SELECT, ID = 2 ) COORDINATE( ACTIVATE ) POINT( ADD, COOR ) 0 0 0 $A $B 0 $B $A COORDINATE( SELECT, ID = 3 ) COORDINATE( ACTIVATE ) POINT( ADD, COOR ) 0 0 0 $A $B 0 $B $A / 920: inlet tube and nozzle head COORDINATE( SELECT, ID = 4 ) COORDINATE( ACTIVATE ) POINT( ADD, COOR ) 0 0 $G 0 $H 0 $H $E $H $F $G $E $G ($L$Q$P$N/2) $G $L 0 $L 0 ($L$P) 0 ($M+$Q+$N) 0 ($M+$Q) 0 $M // ADD CURVES / 13: ellipsoidal top, cylindrical wall, ellipsoidal bottom POINT( SELE, ID) 1 3 CURVE( ADD, ELLIPSE, ANG1 = 0, ANG2 = 90 ) POINT( SELE, ID)
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Appendix B (Continued) 2152 6 CURVE( ADD, LINE ) POINT( SELE, ID) 5 7 CURVE( ADD, ELLIPSE, ANG1 = 0, ANG2 = 90 ) / 49: centerline, inlet & outlet openings POINT( SELE, ID) 7 9 13 CURVE( ADD, LINE ) CURVE( SELE, ID = 1 ) POINT( SELE, ID = 13 ) CURVE( SPLIT, KEEP ) CURVE( SELE, ID = 10 ) CURVE( DELETE ) / 1018: inlet tube & nozzle head POINT( SELE, ID) 12 14 10 CURVE( ADD, LINE ) POINT( SELE, ID) 14 21 9 CURVE( ADD, LINE ) // ADD SURFACES POINT(SELECT, ID ) 4 8 3 7 SURFACE( ADD, POINT, ROWW = 2, NOADDCURVES, INVISIBLE ) // ADD MESH EDGES $NL = 19 DECLARE $LL[1:$NL] DECLARE $MM[1:$NL] $LL[1] = PI*(3*($A+$B)SQRT(($A+3*$B)*(3*$A+$B)))/4 $LL[2] = $C $LL[3] = $LL[1] $LL[4] = 2*$B+$C$H $LL[5] = $G
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Appendix B (Continued) 216$LL[6] = $H$G $LL[7] = $E $LL[8] = $F$E $LL[9] = $LL[1]$F $LL[10] = $H$G $LL[11] = $E $LL[13] = $Q+$P+$N/2 $LL[12] = $L$E$LL[13] $LL[14] = $G $LL[15] = $P $LL[16] = $L$M$N$P$Q $LL[17] = $N $LL[18] = $Q $LL[19] = $M DO( $I = 1, $I .LE. $NL ) IF (($I.EQ.15).OR.($I.EQ.17).OR.($I.EQ.19)) $MM[$I] = 2*INT($LL[$I]/2/$S3+1.5) ELSE IF (($I.EQ.7).OR.($I.EQ.8).OR.($I.EQ.14)) $MM[$I] = 2*INT($LL[$I]/2/$S2+1.5) ELSE $MM[$I] = 2*INT($LL[$I]/2/$S1+1.5) ENDIF ENDIF ENDDO $MM[5] = $MM[14] $MM[11] = $MM[7] $MM[13] = $MM[15]+$MM[16]+$MM[17]/2 $MM[12] = $MM[19]+$MM[18]+$MM[17]/2$MM[11] // ADD MESH EDGES CURVE( SELECT, ID = 1 ) MEDGE( ADD, SUCC, INTE = $MM[1], RATI = 0, 2RAT = 0, PCEN = 0, INVISIBLE ) DO( $I = 2, $I .LE. $NL ) CURVE( SELECT, ID = $I ) IF (($I.EQ.15).OR.($I.EQ.17).OR.($I.EQ.19)) MEDGE( ADD, SUCC, INTE = $MM[$I], RATI = 0, 2RAT = 0, PCEN = 0 ) ELSE MEDGE( ADD, FRTL, INTE = $MM[$I], RATI = $S3, 2RAT = $S3, PCEN = 0 ) ENDIF ENDDO // ADD MESH LOOPS / 1: inlet tube CURVE( SELECT, ID ) 6 7 10 11
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Appendix B (Continued) 217MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) / 2: nozzle head CURVE( SELECT, ID ) 11 19 5 MLOOP( ADD, MAP, EDG1 = 3, EDG2 = 1, EDG3 = 5, EDG4 = 1 ) / 3: tank space CURVE( SELECT, ID ) 4 3 2 9 8 10 12 19 MLOOP( ADD, PAVE ) // ADD MESH FACES $NML = LASTID( MLOOP_ID ) DO( $I = 1, $I .LE. $NML ) SURFACE( SELECT, ID = 1) MLOOP( SELECT, ID = $I) MFACE( ADD ) ENDDO // ADD BOUNDARY EDGE MFACE( SELECT, ID = 3 ) CURVE( SELECT, ID ) 2 3 4 8 10 12 19 BEDGE( ADD, 1HEIGHT = $S3, GROWTH = $BG, LAYERS = $BL, INVISIBLE ) // GENERATE MESH MFACE( SELECT, ID ) 1 2 MFACE( MESH, MAP, ENTI = "fluid" ) MFACE( SELECT, ID = 3 ) MFACE( MESH, PAVE, ENTI = "fluid" ) // GENERATE EDGE MESH ELEMENT( SETD, EDGE, NODE = 2 ) MEDGE( SELECT, ID = 7 ) MEDGE( MESH, MAP, ENTI = "inlet" )
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Appendix B (Continued) 218MEDGE( SELECT, ID = 8 ) MEDGE( MESH, MAP, ENTI = "outlet" ) MEDGE( SELECT, ID ) 9 2 3 MEDGE( MESH, MAP, ENTI = "tk_wall" ) MEDGE( SELECT, ID ) 4 6 MEDGE( MESH, MAP, ENTI = "tk_axis" ) MEDGE( SELECT, ID ) 10 12 14 16 18 MEDGE( MESH, MAP, ENTI = "nz_wall" ) MEDGE( SELECT, ID ) 15 19 2 MEDGE( MESH, MAP, ENTI = "nozzles" ) MEDGE( SELECT, ID = 1 ) MEDGE( MESH, REMOVE ) MEDGE( SELECT, ID = 1 ) MEDGE( DELETE ) END B.2 Simulation Settings: FIDAP Commands / FIDAP Input File / SIMULATION SETTINGS / PROJECT: Cryogenic LH2 Tank with Injection Nozzles / Axisymmetric model, SI units / $V0 = 0.01 $F0 = 1.0 $T0 = 18 / TITLE LH2 tank w/ displacement cooling nozzle system FIPREP / / MATERIAL PROPERTIES / / Properties of Liquid Hydrogen at Reference Temperature: Tref = 20K DENSITY( SET = "LH2", CONS = 71.1 ) VISCOSITY( SET = "LH2", CONS = 13.6E6, MIXLENGTH )
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Appendix B (Continued) 219SPECIFICHEAT( SET = "LH2", CONS = 9.53E3 ) CONDUCTIVITY( SET = "LH2", CONS = 0.0984 ) / / CONTINUUM ENTITIES / ENTITY( NAME = "fluid", FLUID, PROPERTY = "LH2" ) / / BOUNDARY ENTITIES / ENTITY( NAME = "inlet", PLOT ) ENTITY( NAME = "outlet", PLOT ) ENTITY( NAME = "tk_axis", PLOT ) ENTITY( NAME = "tk_wall", WALL ) ENTITY( NAME = "nz_wall", WALL ) ENTITY( NAME = "nozzles", PLOT ) / / INITIAL AND BOUNDARY CONDITIONS ICNODE( TEMP, ALL, CONS = $T0 ) / BCNODE( UY, ENTI = "tk_axis", ZERO ) BCNODE( VELO, ENTI = "tk_wall", ZERO ) BCNODE( VELO, ENTI = "nz_wall", ZERO ) BCNODE( VELO, ENTI = "inlet", X = $V0, Y = 0 ) / BCFLUX( HEAT, ENTI = "tk_wall", CONS = $F0 ) BCNODE( TEMP, ENTI = "inlet", CONS = $T0 ) / / PROBLEM SETUP / PROBLEM( AXI, TURBULENT, NONLINEAR, ENERGY ) EXECUTION( NEWJOB ) DATAPRINT( NONE ) PRINTOUT( NONE ) / / SOLUTION PARAMETERS / SOLUTION( S.S. = 64, VELCONV = 1E4, RESCONV = 1E4 ) PRESSURE( MIXED = 1E8, DISCONTINUOUS ) OPTIONS( UPWINDING ) CLIPPING( MINIMUM ) 0 0 0 0 $T0 / END / CREATE( FISOLV ) RUN( FISOLV, BACK )
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220 Appendix C: FIDAP Preprocessing Input for Chapter 4 C.1 Geometry and Meshing: FIDAP Commands / FIDAP Input File / GEOMETRY and MESHING / PROJECT: Cryogenic LH2 Tank with Array of PumpNozzle Units / Axisymmetric model, SI units / / $G: gap between heat pipe and nozzle face, 0.1, 0.2, 0.3 / $H: length of heat pipe, 1.0, 1.5, 2.0 / $P: distance from inlet opening to pump center, 0.25, 0.55, 0.85 $G = 0.2 $H = 1.5 $P = 0.55 / TITLE LH2 tank w/ heat pipe & array of pumpnozzle units // FIGEN FIGEN( ELEM = 1, POIN = 1, CURV = 1, SURF = 1, NODE = 0, MEDG = 1, MLOO = 1, MFAC = 1, BEDG = 1, SPAV = 1, MSHE = 1, MSOL = 1, COOR = 1 ) // DEFINE DIMENSIONS $A = 1.5 $B = 0.65 $C = 1.3 $D = 0.2 $E = 0.3 $F = $D/2 $K = SQRT($A^2$F^2)*$B/$A $L = 0.3 $M = 0.1 $N = 0.1 $O = 0.1 $R = 0.1 $S = SQRT($R^2$O^2/4) $T = SQRT($R^2$N^2/4) // DEFINE COORDINATE SYSTEMS COORDINATE( ADD, ROTATION, SYSTEM = 2 ) $B 0 0 2 180 COORDINATE( ADD, ROTATION, SYSTEM = 3 ) ($B+$C) 0 0 COORDINATE( ADD, ROTATION, SYSTEM = 4 ) ($H$E+$M/2+$O/2) ($F+$G+$L) 0 1 180 2 180 // ADD POINTS COORDINATE( SELECT, ID = 2 ) COORDINATE( ACTIVATE )
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Appendix C (Continued) 221POINT( ADD, COOR ) 0 0 0 $A $B 0 $B $A COORDINATE( SELECT, ID = 3 ) COORDINATE( ACTIVATE ) POINT( ADD, COOR ) 0 0 0 $A $B 0 $B $A COORDINATE( SELECT, ID = 1 ) COORDINATE( ACTIVATE ) POINT( ADD, COOR ) ($H$F) 0 $H 0 ($H$F) $F ($H$E) $F ($B$K) $F COORDINATE( SELECT, ID = 4 ) COORDINATE( ACTIVATE ) POINT( ADD, COOR ) 0 0 ($O/2) ($L$M) ($O/2) $S $T ($N/2) $P ($N/2) $P ($N/2) $T ($N/2) ($O/2) $S ($O/2) ($L$M) / 2328 ($O/2+$M/2) ($L$M/2) ($O/2+$M/2) $L ($O/2$M/2) $L ($O/2$M/2) ($L$M/2) ($O/2) ($L$M/2) ($O/2) ($L$M/2) // ADD CURVES POINT( SELE, ID) 1 3 CURVE( ADD, ELLIPSE, ANG1 = 0, ANG2 = 90 ) POINT( SELE, ID) 2 6
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Appendix C (Continued) 222CURVE( ADD, LINE ) POINT( SELE, ID) 5 7 CURVE( ADD, ELLIPSE, ANG1 = 0, ANG2 = 90 ) POINT( SELE, ID) 7 10 CURVE( ADD, LINE ) POINT( SELE, ID) 9 11 CURVE( ADD, ARC, CENTER2POINTS, MINARC ) POINT( SELE, ID) 11 13 CURVE( ADD, LINE ) CURVE( SELE, ID = 1 ) POINT( SELE, ID = 13 ) CURVE( SPLIT, KEEP ) CURVE( SELE, ID = 9 ) CURVE( DELETE ) POINT( SELE, ID) 15 16 CURVE( ADD, LINE ) POINT( SELE, ID) 14 16 17 CURVE( ADD, ARC, CENTER2POINTS, MAXARC ) POINT( SELE, ID) 17 20 CURVE( ADD, LINE ) POINT( SELE, ID) 14 20 21 CURVE( ADD, ARC, CENTER2POINTS, MINARC ) POINT( SELE, ID) 21 22 CURVE( ADD, LINE ) POINT( SELE, ID) 28 22 23 CURVE( ADD, ARC, CENTER2POINTS, MINARC )
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Appendix C (Continued) 223POINT( SELE, ID) 23 26 CURVE( ADD, LINE ) POINT( SELE, ID) 27 26 15 CURVE( ADD, ARC, CENTER2POINTS, MINARC ) // ADD SURFACES POINT(SELECT, ID ) 4 8 3 7 SURFACE( ADD, POINT, ROWW = 2, NOADDCURVES, INVISIBLE ) // ADD MESH EDGES $NL = 20 DECLARE $LL[1:$NL] DECLARE $MM[1:$NL] $LL[1] = PI*(3*($A+$B)SQRT(($A+3*$B)*(3*$A+$B)))/4 $LL[2] = $C $LL[3] = $LL[1] $LL[4] = 2*$B+$C$H $LL[5] = PI*$F/2 $LL[6] = $E$F $LL[7] = $H$E $LL[8] = $LL[1]$F $LL[9] = $L$M$S $LL[10] = (3*1802*ACOS($S/$R)2*ACOS($T/$R))*DEG2RAD*$R/2 $LL[11] = $P$T $LL[12] = $N $LL[13] = $LL[11] $LL[14] = (1802*ACOS($S/$R)2*ACOS($T/$R))*DEG2RAD*$R/2 $LL[15] = $LL[9] $LL[16] = PI*$M/4 $LL[17] = $M/2 $LL[18] = ($O+$M) $LL[19] = $LL[17] $LL[20] = $LL[16] $S1 = 0.02 $S2 = 0.01000001 DO( $I = 1, $I .LE. 8 ) $MM[$I] = 2*INT($LL[$I]/2/$S1+1.5) ENDDO
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Appendix C (Continued) 224DO( $I = 5, $I .LE. 6 ) $MM[$I] = 2*INT($LL[$I]/2/$S2+1.5) ENDDO DO( $I = 9, $I .LE. $NL ) $MM[$I] = 2*INT($LL[$I]/2/$S2+1.5) ENDDO // ADD MESH EDGES CURVE( SELECT, ID = 1 ) MEDGE( ADD, SUCC, INTE = $MM[1], RATI = 0, 2RAT = 0, PCEN = 0, INVISIBLE ) DO( $I = 2, $I .LE. $NL ) CURVE( SELECT, ID = $I ) MEDGE( ADD, LSTF, INTE = $MM[$I], RATI = 2, 2RAT = 2, PCEN = 0 ) ENDDO // ADD MESH LOOPS / 1: tank boundary CURVE( SELECT, ID ) 2 8 MLOOP( ADD, PAVE ) / 2: pumpnozzle unit boundary CURVE( SELECT, ID ) 9 24 MLOOP( ADD, PAVE ) // ADD MESH FACES SURFACE( SELECT, ID = 1) MLOOP( SELECT, ID ) 1 2 MFACE( ADD ) // ADD BOUNDARY EDGE MFACE( SELECT, ID = 1 ) CURVE( SELECT, ID ) 2 20 BEDGE( ADD, 1HEIGHT = 0.005, GROWTH = 1.1, LAYERS = 3, INVISIBLE ) // GENERATE MESH MFACE( SELECT, ID = 1) MFACE( MESH, PAVE, ENTI = "fluid" ) // GENERATE EDGE MESH ELEMENT( SETD, EDGE, NODE = 2 )
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Appendix C (Continued) 225MEDGE( SELECT, ID ) 2 3 8 MEDGE( MESH, MAP, ENTI = "tk_wall" ) MEDGE( SELECT, ID = 4 ) MEDGE( MESH, MAP, ENTI = "tk_symm" ) MEDGE( SELECT, ID ) 5 6 MEDGE( MESH, MAP, ENTI = "hp_evap" ) MEDGE( SELECT, ID = 7 ) MEDGE( MESH, MAP, ENTI = "hp_insu" ) MEDGE( SELECT, ID = 12 ) MEDGE( MESH, MAP, ENTI = "pp_inlet" ) MEDGE( SELECT, ID = 18 ) MEDGE( MESH, MAP, ENTI = "pp_outlet" ) MEDGE( SELECT, ID ) 9 11 13 17 19 20 MEDGE( MESH, MAP, ENTI = "pp_wall" ) MEDGE( SELECT, ID = 1 ) MEDGE( MESH, REMOVE ) MEDGE( SELECT, ID = 1 ) MEDGE( DELETE ) / END C.2 Simulation Settings: FIDAP Commands / FIDAP Input File / SIMULATION SETTINGS / PROJECT: Cryogenic LH2 Tank with Array of PumpNozzle Units / Axisymmetric model, SI units / / $F0 = 1.0 $T0 = 20 / $NS = 5 $V0 = 0.05 / TITLE LH2 tank w/ heat pipe & array of pumpnozzle units /
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Appendix C (Continued) 226FIPREP / / MATERIAL PROPERTIES / DENSITY( SET = "LH2", CONSTANT = 70.8 ) VISCOSITY( SET = "LH2", CONSTANT = 13.2E6, MIXLENGTH ) CONDUCTIVITY( SET = "LH2", CONSTANT = 0.0989 ) SPECIFICHEAT( SET = "LH2", CONSTANT = 9.66E3 ) / / CONTINUUM ENTITIES / ENTITY ( NAME = "fluid", FLUID, PROPERTY = "LH2" ) / / BOUNDARY ENTITIES / ENTITY ( NAME = "tk_wall", WALL ) ENTITY ( NAME = "tk_symm", PLOT ) ENTITY ( NAME = "hp_evap", WALL ) ENTITY ( NAME = "hp_insu", WALL ) ENTITY ( NAME = "pp_wall", WALL ) ENTITY ( NAME = "pp_inlet", PLOT ) ENTITY ( NAME = "pp_outlet", PLOT ) / / DEFINE TIME (LOAD) FUNCTIONS / TMFUNCTION ( SET = 1, LINEAR, ACOEF = 1, BCOEF = 0 ) / / INITIAL AND BOUNDARY CONDITIONS / BCNODE( VELO, ZERO, ENTITY = "tk_wall" ) BCNODE( UY, ZERO, ENTITY = "tk_symm" ) BCNODE( VELO, ZERO, ENTITY = "hp_evap" ) BCNODE( VELO, ZERO, ENTITY = "hp_insu" ) BCNODE( VELO, ZERO, ENTITY = "pp_wall" ) BCNODE( UX, ZERO, ENTITY = "pp_outlet" ) BCNODE( UY, CONSTANT = $V0, ENTITY = "pp_outlet" ) BCFLUX( HEAT, CONST = $F0, CURVE = 1, ENTITY = "tk_wall" ) BCNODE( TEMP, CONST = $T0, CURVE = 1, ENTITY = "hp_evap" ) / / PROBLEM SETUP / PROBLEM( AXI, TURBULENT, NONLINEAR, ENERGY ) EXECUTION( NEWJOB ) PRINTOUT( NONE ) DATAPRINT( NONE ) / / SOLUTION PARAMETERS /
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Appendix C (Continued) 227SOLUTION( S.S. = 64, VELCONV = 1.E6, RESCONV = 1.E6 ) PRESSURE( MIXED = 1.E8, DISCONTINUOUS ) INCREMENTAL( NLSTEPS = $NS, BDRYCDTNS ) / END / CREATE( FISOLV ) RUN( FISOLV, BACK )
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228 Appendix D: GAMBIT/FIDAP Preprocessing Input for Chapter 5 D.1 Geometry and Meshing: GAMBIT Commands / GAMBIT Input File / GEOMETRY and MESHING / PROJECT: Cryogenic LH2 Tank with Lateral PumpNozzle Unit / Threedimensional (3D) model, SI units / / CREATING THE GEOMETRY / / Tank: cylindrical body + spheroidal top and bottom / vertex create coordinates 0 0 0 vertex create coordinates 0 0 0.65 vertex create coordinates 0 0 1.95 vertex create coordinates 0 0 2.6 vertex create coordinates 1.5 0 1.95 vertex create coordinates 1.5 0 0.65 edge create straight "vertex.1" "vertex.4" edge create straight "vertex.6" "vertex.5" edge create center "vertex.2" major "vertex.6" onedge "vertex.1" start 0 end \ 90 ellipse edge create center "vertex.3" major "vertex.5" onedge "vertex.4" start 0 end \ 90 ellipse face create wireframe "edge.1" "edge.2" "edge.3" "edge.4" real volume create revolve "face.1" dangle 180 vector 0 0 1 origin 0 0 0 / / Heat pipe: cylindrical body + spherical tip / coordinate create cartesian oldsystem "c_sys.1" offset 0 0 2.6 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation coordinate activate "c_sys.2" volume create height 1.4 radius1 0.1 radius3 0.1 offset 0 0 0.7 zaxis frustum volume create radius 0.1 sphere volume move "volume.3" offset 0 0 1.4 volume unite volumes "volume.2" "volume.3" volume subtract "volume.1" volumes "volume.2" / / Pumpnozzle unit: sph. body + cyl. inlet tube + nozzle head / coordinate create cartesian oldsystem "c_sys.2" offset 0.3 0 1.3 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation coordinate activate "c_sys.3" volume create height 0.05 radius1 0.1 radius3 0.1 offset 0.025 0 0 xaxis frustum volume create radius1 0.05 radius2 0.05 xaxis torus volume move "volume.3" offset 0.05 0 0
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Appendix D (Continued) 229volume create height 0.25 radius1 0.05 radius3 0.05 offset 0.125 0 0 xaxis frustum volume unite volumes "volume.4" "volume.3" "volume.2" volume create radius 0.1 sphere volume move "volume.5" offset 0.3 0 0 volume create height 0.8 radius1 0.05 radius3 0.05 offset 0 0 0.4 zaxis frustum volume move "volume.6" offset 0.3 0 0 volume unite volumes "volume.4" "volume.5" "volume.6" volume subtract "volume.1" volumes "volume.4" / / SUBDIVIDING THE VOLUME / coordinate activate "c_sys.2" volume create width 0.3 depth 0.3 height 1.55 offset 0.15 0.15 0.775 brick volume move "volume.2" offset 0.15 0.15 0 face cmove "face.29" multiple 1 offset 0 0 0.15 face cmove "face.35" multiple 1 offset 0 0 0.2 volume split "volume.1" volumes "volume.2" connected volume split "volume.3" faces "face.36" connected volume split "volume.4" faces "face.35" connected face cmove "face.37" multiple 1 offset 0.3 0 0.1 face cmove "face.37" multiple 1 offset 0.3 0 0.4 edge split "edge.90" vertex "vertex.71" connected edge split "edge.88" vertex "vertex.72" connected edge split "edge.69" vertex "vertex.75" connected edge split "edge.67" vertex "vertex.76" connected edge create straight "vertex.70" "vertex.74" edge create straight "vertex.73" "vertex.77" face create wireframe "edge.100" "edge.109" "edge.104" "edge.110" real face create wireframe "edge.97" "edge.90" "edge.78" "edge.107" "edge.101" \ "edge.109" real face create wireframe "edge.88" "edge.76" "edge.108" "edge.103" "edge.110" \ "edge.99" real face split "face.48" connected keeptool face "face.53" face split "face.31" connected keeptool face "face.54" volume create stitch "face.59" "face.42" "face.31" "face.54" "face.55" \ "face.53" "face.56" "face.57" real / coordinate activate "c_sys.3" volume create width 0.3 depth 0.15 height 1.1 offset 0.15 0.075 0.55 brick volume move "volume.7" offset 0.15 0 0.15 volume unite volumes "volume.6" "volume.7" volume split "volume.1" volumes "volume.6" connected volume create width 0.4 depth 0.2 height 0.4 offset 0.2 0.1 0.2 brick volume move "volume.8" offset 0.15 0 0.15
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Appendix D (Continued) 230volume split "volume.7" volumes "volume.8" connected face cmove "face.67" multiple 1 offset 0 0 0.15 volume split "volume.7" faces "face.88" connected face cmove "face.39" multiple 1 offset 0.15 0 0 volume split "volume.5" faces "face.94" connected volume create radius 0.1 sphere face cmove "face.82" multiple 1 offset 0.15 0 0 edge create straight "vertex.136" "vertex.133" "vertex.131" "vertex.132" edge create straight "vertex.132" "vertex.136" face delete "face.101" lowertopology face create wireframe "edge.211" "edge.212" "edge.213" "edge.214" real face cmove "face.101" multiple 1 offset 0.05 0 0 volume split "volume.10" faces "face.101" connected volume split "volume.10" faces "face.102" connected volume split "volume.14" volumes "volume.13" connected face cmove "face.107" multiple 1 offset 0 0 0.15 volume split "volume.14" faces "face.114" connected keeptool volume split "volume.13" faces "face.114" connected face cmove "face.92" multiple 1 offset 0.15 0 0 / coordinate create cartesian oldsystem "c_sys.3" offset 0.3 0 0.8 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation coordinate activate "c_sys.4" volume create radius 0.05 sphere volume split "volume.11" volumes "volume.19" connected volume split "volume.19" faces "face.123" connected keeptool volume split "volume.11" faces "face.123" connected face cmove "face.81" multiple 1 offset 0.15 0 0 face cmove "face.53" multiple 1 offset 0 0 0.15 volume split "volume.8" faces "face.134" connected volume split "volume.23" faces "face.135" connected keeptool volume split "volume.8" faces "face.135" connected face cmove "face.78" multiple 1 offset 0 0 0.15 volume split "volume.10" faces "face.154" connected vertex delete "vertex.3" "vertex.2" / face create plane "vertex.77" "vertex.95" "vertex.195" face create plane "vertex.77" "vertex.189" "vertex.208" face create plane "vertex.77" "vertex.196" "vertex.208" face split "face.160" connected keeptool face "face.161" face delete "face.163" lowertopology face unite faces "face.161" "face.160" real face split "face.148" connected face "face.161" face split "face.148" connected face "face.160" face split "face.148" connected face "face.162" / edge create straight "vertex.214" "vertex.77" edge create straight "vertex.215" "vertex.189" edge create straight "vertex.222" "vertex.196" edge create straight "vertex.219" "vertex.95"
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Appendix D (Continued) 231face create wireframe "edge.344" "edge.350" "edge.298" "edge.351" real face create wireframe "edge.349" "edge.350" "edge.166" "edge.352" real face create wireframe "edge.346" "edge.350" "edge.104" "edge.353" real face unite faces "face.165" "face.166" real volume split "volume.24" faces "face.166" connected volume split "volume.24" faces "face.165" connected volume split "volume.27" faces "face.167" connected / face create plane "vertex.110" "vertex.111" "vertex.195" face create plane "vertex.200" "vertex.110" "vertex.223" face split "face.171" connected keeptool face "face.172" face delete "face.171" lowertopology face split "face.172" connected keeptool face "face.173" face delete "face.175" lowertopology face unite faces "face.172" "face.173" real volume split "volume.25" faces "face.172" connected volume split "volume.25" faces "face.173" connected face create plane "vertex.110" "vertex.227" "vertex.199" volume split "volume.25" faces "face.178" connected / face create plane "vertex.106" "vertex.196" "vertex.186" face create plane "vertex.106" "vertex.107" "vertex.195" face split "face.183" connected face "face.182" face delete "face.182" lowertopology volume split "volume.23" faces "face.183" connected face create plane "vertex.106" "vertex.241" "vertex.185" volume split "volume.23" faces "face.186" connected edge create straight "vertex.222" "vertex.241" face create wireframe "edge.413" "edge.402" "edge.306" "edge.357" real volume split "volume.23" faces "face.190" connected / vertex cmove "vertex.61" multiple 1 offset 0 0 0.05 edge split "edge.68" vertex "vertex.247" connected vertex cmove "vertex.65" multiple 1 offset 0 0 0.05 edge split "edge.86" vertex "vertex.248" connected / coordinate activate "c_sys.1" volume create width 1.6 depth 1.6 height 6 brick volume split "volume.1" volumes "volume.33" connected edge create straight "vertex.8" "vertex.5" edge create straight "vertex.7" "vertex.6" face create wireframe "edge.8" "edge.446" real face create wireframe "edge.6" "edge.447" real volume split "volume.1" faces "face.205" connected volume split "volume.35" faces "face.206" connected / vertex cmove "vertex.94" multiple 1 offset 0.05 0 0 edge split "edge.449" vertex "vertex.277" connected edge create straight "vertex.94" "vertex.277"
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Appendix D (Continued) 232face split "face.203" virtual edges "edge.469" / / MESHING THE MODEL / blayer create first 0.01 growth 1.2 total 0.022 rows 2 transition 1 trows 0 blayer attach "b_layer.1" face "face.134" "face.146" "face.165" "face.166" \ "face.169" "face.27" "face.170" "face.167" "face.85" "face.147" "face.168" \ edge "edge.313" "edge.348" "edge.344" "edge.349" "edge.345" "edge.39" \ "edge.347" "edge.346" "edge.37" "edge.35" "edge.310" / blayer create first 0.01 growth 1.2 total 0.022 rows 2 transition 1 trows 0 blayer attach "b_layer.2" face "face.140" "face.134" "face.152" "face.179" \ "face.137" "face.177" "face.173" "face.175" "face.181" edge "edge.296" \ "edge.313" "edge.319" "edge.392" "edge.384" "edge.29" "edge.385" "edge.383" \ "edge.393" / blayer create first 0.01 growth 1.2 total 0.022 rows 2 transition 1 trows 0 blayer attach "b_layer.3" face "face.168" "face.83" "face.79" "face.184" \ "face.143" "face.189" "face.191" "face.185" "face.187" edge "edge.310" \ "edge.25" "edge.405" "edge.293" "edge.294" "edge.412" "edge.417" "edge.404" \ "edge.411" / blayer create first 0.01 growth 1.2 total 0.022 rows 2 transition 1 trows 0 blayer attach "b_layer.4" face "face.149" edge "edge.316" / blayer create first 0.01 growth 1.2 total 0.022 rows 2 transition 1 trows 0 blayer attach "b_layer.5" face "face.141" "face.77" "face.88" "face.130" \ edge "edge.174" "edge.300" "edge.268" "edge.43" / blayer create first 0.01 growth 1.2 total 0.022 rows 2 transition 1 trows 0 blayer attach "b_layer.6" \ face "face.82" "face.145" "face.104" "face.104" "face.157" "face.157" \ "face.111" "face.111" "face.159" "face.102" "face.120" "face.101" \ edge "edge.312" "edge.167" "edge.28" "edge.164" "edge.329" "edge.330" \ "edge.38" "edge.36" "edge.32" "edge.326" "edge.33" "edge.247"
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Appendix D (Continued) 233/ blayer create first 0.01 growth 1.2 total 0.022 rows 2 transition 1 trows 0 blayer attach "b_layer.7" face "face.49" "face.99" "face.96" "face.47" \ "face.94" "face.36" "face.40" edge "edge.10" "edge.204" "edge.12" \ "edge.201" "edge.200" "edge.81" "edge.16" / blayer create first 0.01 growth 1.2 total 0.022 rows 2 transition 1 trows 0 blayer attach "b_layer.8" face "face.44" "face.61" "face.30" "face.43" \ "face.45" "face.46" edge "edge.15" "edge.72" "edge.74" "edge.73" "edge.75" \ "edge.16" / blayer create first 0.01 growth 2 total 0.03 rows 2 transition 1 trows 0 blayer attach "b_layer.9" face "face.210" "face.209" "face.211" \ "face.202" "face.205" "face.71" edge "edge.442" \ "edge.444" "edge.443" "edge.441" "edge.8" "edge.4" / blayer create first 0.01 growth 2 total 0.03 rows 2 transition 1 trows 0 blayer attach "b_layer.10" face "face.212" "face.213" \ "face.196" "face.208" "face.215" "face.214" edge \ "edge.435" "edge.434" "edge.436" "edge.3" "edge.6" "edge.5" / blayer create first 0.01 growth 2 total 0.03 rows 2 transition 1 trows 0 blayer attach "b_layer.11" face "v_face.218" "v_face.219" edge "edge.71" \ "edge.445" / face modify "face.146" side "vertex.196" face modify "face.134" side "vertex.189" face modify "face.85" side "vertex.95" face modify "face.164" end "vertex.214" face modify "face.82" end "vertex.196" face modify "face.141" end "vertex.189" face modify "face.170" end "vertex.33" face modify "face.85" end "vertex.30" face modify "face.168" end "vertex.24" face modify "face.82" side "vertex.77" / edge mesh "edge.344" "edge.346" "edge.349" successive ratio1 1 intervals 3 edge mesh "edge.348" "edge.313" successive ratio1 1 intervals 3 edge mesh "edge.345" "edge.347" "edge.37" "edge.310" successive ratio1 1 \ intervals 4 edge mesh "edge.39" "edge.35" successive ratio1 1 intervals 6 edge mesh "edge.174" "edge.312" successive ratio1 1 intervals 6
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Appendix D (Continued) 234edge mesh "edge.104" "edge.298" "edge.166" "edge.307" successive \ ratio1 1 intervals 3 edge mesh "edge.169" "edge.311" successive ratio1 1 intervals 4 edge mesh "edge.308" successive ratio1 1 intervals 4 / face modify "face.177" end "vertex.32" face modify "face.77" side "vertex.110" face modify "face.180" end "vertex.227" face modify "face.169" end "vertex.188" face modify "face.141" side "vertex.77" / edge mesh "edge.297" "edge.42" "edge.171" successive ratio1 1 intervals 4 edge mesh "edge.172" "edge.173" "edge.168" "edge.165" "edge.295" "edge.317" \ "edge.318" successive ratio1 1 intervals 3 edge mesh "edge.300" "edge.296" successive ratio1 1 intervals 6 edge mesh "edge.299" "edge.176" "edge.309" "edge.170" "edge.175" successive \ ratio1 1 intervals 4 edge mesh "edge.29" successive ratio1 1 intervals 4 edge mesh "edge.383" "edge.319" "edge.393" successive ratio1 1 intervals 3 edge mesh "edge.385" "edge.384" "edge.392" successive ratio1 1 intervals 3 / volume mesh "volume.29" map volume mesh "volume.30" map volume mesh "volume.25" map volume mesh "volume.24" map volume mesh "volume.28" map volume mesh "volume.27" map / face modify "face.168" end "vertex.24" face modify "face.79" end "vertex.28" face modify "face.145" side "vertex.106" face modify "face.192" end "vertex.241" face modify "face.149" side "vertex.94" / edge mesh "edge.167" "edge.25" successive ratio1 1 intervals 6 edge mesh "edge.161" "edge.306" "edge.307" "edge.160" "edge.291" "edge.290" \ "edge.305" successive ratio1 1 intervals 3 edge mesh "edge.404" "edge.417" "edge.411" successive ratio1 1 intervals 3 edge mesh "edge.315" "edge.143" "edge.289" "edge.314" "edge.122" successive \ ratio1 1 intervals 3 edge mesh "edge.316" successive ratio1 1 intervals 6 / volume mesh "volume.23" map volume mesh "volume.32" "volume.31" map volume mesh "volume.24" map
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Appendix D (Continued) 235volume mesh "volume.28" map volume mesh "volume.30" map volume mesh "volume.8" cooper source "face.139" "face.53" "face.150" \ "face.151" / face modify "face.102" side "vertex.145" face modify "face.102" end "vertex.206" face modify "face.157" end "vertex.198" face modify "face.157" side "vertex.196" face modify "face.104" side "vertex.107" face modify "face.159" side "vertex.147" face modify "face.111" side "vertex.95" / edge mesh "edge.329" successive ratio1 1 intervals 6 edge mesh "edge.28" successive ratio1 1 intervals 6 edge mesh "edge.228" "edge.327" "edge.162" successive ratio1 1 intervals 2 / volume mesh "volume.10" cooper source "face.111" "face.157" volume mesh "volume.26" cooper source "face.104" "face.157" volume mesh "volume.23" "volume.28" map / edge mesh "edge.33" "edge.247" successive ratio1 1 intervals 6 / face modify "face.159" end "vertex.147" face modify "face.102" end "vertex.145" / volume mesh "volume.15" cooper source "face.102" "face.101" "face.159" \ "face.120" / edge mesh "edge.268" "edge.43" successive ratio1 1 intervals 6 edge mesh "edge.273" "edge.263" "edge.272" successive ratio1 1 intervals 6 edge mesh "edge.274" "edge.187" "edge.126" "edge.278" "edge.131" "edge.147" \ "edge.279" "edge.276" "edge.190" successive ratio1 1 intervals 3 edge mesh "edge.280" "edge.129" "edge.130" "edge.125" "edge.186" "edge.145" \ "edge.185" "edge.276" "edge.279" "edge.147" "edge.131" "edge.278" \ "edge.126" "edge.187" "edge.274" "edge.190" successive ratio1 1 intervals 3 edge mesh "edge.277" "edge.275" "edge.188" "edge.189" successive ratio1 1 \ intervals 4 / volume mesh "volume.7" cooper source "face.88" "face.130" "face.77" \ "face.141" size 0.07 / face modify "face.131" side "vertex.97" face modify "face.123" side "vertex.175" face modify "face.88" side "vertex.119"
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Appendix D (Continued) 236/ volume mesh "volume.11" cooper source "face.129" "face.133" "face.91" \ "face.93" / face modify "face.125" side "vertex.96" face modify "face.130" side "vertex.118" / volume mesh "volume.22" cooper source "face.124" "face.92" "face.132" \ "face.67" / edge mesh "edge.271" "edge.270" "edge.269" "edge.44" successive ratio1 1 intervals 4 / volume mesh "volume.19" "volume.21" tetprimitive / edge mesh "edge.237" "edge.253" "edge.255" successive ratio1 1 intervals 6 edge mesh "edge.249" "edge.248" "edge.78" "edge.76" successive ratio1 1 \ intervals 2 edge mesh "edge.254" successive ratio1 1 intervals 3 / face modify "face.116" side "vertex.71" face modify "face.101" side "vertex.141" face modify "face.115" side "vertex.158" face modify "face.113" side "vertex.75" face modify "face.120" side "vertex.143" / volume mesh "volume.14" cooper source "face.117" "face.105" "face.118" \ "face.59" "face.103" volume mesh "volume.17" cooper source "face.100" "face.107" "face.42" \ "face.31" "face.119" / edge mesh "edge.257" "edge.258" "edge.256" "edge.34" successive ratio1 1 \ intervals 4 / volume mesh "volume.13" "volume.18" tetprimitive / edge mesh "edge.10" "edge.204" "edge.12" "edge.201" "edge.200" successive \ ratio1 1 intervals 6 edge mesh "edge.93" "edge.91" "edge.89" "edge.45" "edge.65" "edge.70" \ "edge.197" "edge.196" "edge.199" "edge.202" "edge.195" "edge.66" "edge.46" \ successive ratio1 1 intervals 3 edge mesh "edge.105" successive ratio1 1 intervals 2 /
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Appendix D (Continued) 237face modify "face.47" side "vertex.55" face modify "face.49" side "vertex.67" face modify "face.94" side "vertex.126" face modify "face.96" side "vertex.54" face modify "face.99" side "vertex.66" / volume mesh "volume.12" cooper source "face.10" "face.39" "face.97" "face.95" volume mesh "volume.5" cooper source "face.98" "face.41" "face.37" "face.48" \ "face.59" / edge mesh "edge.81" successive ratio1 1 intervals 12 / face modify "face.99" end "vertex.66" face modify "face.49" end "vertex.67" / volume mesh "volume.4" cooper source "face.49" "face.99" "face.36" / edge mesh "edge.16" successive ratio1 1 intervals 12 volume mesh "volume.3" cooper source "face.36" "face.40" size 0.07 / edge mesh "edge.437" "edge.438" successive ratio1 1 intervals 10 / face modify "face.205" side "vertex.267" face modify "face.205" side "vertex.268" face modify "face.204" side "vertex.261" face modify "face.204" side "vertex.262" / volume mesh "volume.1" cooper source "face.202" "face.71" size 0.08 volume delete "volume.1" lowertopology onlymesh / edge mesh "edge.460" "edge.461" successive ratio1 1 intervals 8 edge mesh "edge.6" successive ratio1 1 intervals 48 / face modify "face.215" side "vertex.274" face modify "face.215" side "vertex.273" face modify "face.2" side "vertex.260" face modify "face.2" side "vertex.259" / volume mesh "volume.36" cooper source "face.208" "face.214" size 0.08 volume delete "volume.36" lowertopology onlymesh / edge mesh "edge.71" successive ratio1 1 intervals 13 edge mesh "edge.445" successive ratio1 1 intervals 11 edge mesh "edge.6" successive ratio1 1 intervals 54 / edge mesh "edge.449" successive ratio1 1 intervals 12 edge mesh "edge.469" successive ratio1 1 intervals 1 / edge mesh "edge.460" "edge.461" successive ratio1 1 intervals 8 edge mesh "edge.459" "edge.440" successive ratio1 1 intervals 8 edge mesh "edge.465" "edge.466" successive ratio1 1 intervals 8
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Appendix D (Continued) 238edge mesh "edge.463" "edge.464" successive ratio1 1 intervals 12 / edge mesh "edge.439" "edge.457" successive ratio1 1 intervals 12 edge mesh "edge.455" "edge.456" successive ratio1 1 intervals 8 edge mesh "edge.8" successive ratio1 1 intervals 54 edge mesh "edge.444" successive ratio1 1 intervals 30 edge mesh "edge.442" "edge.443" successive ratio1 1 intervals 12 edge mesh "edge.453" "edge.454" successive ratio1 1 intervals 12 edge mesh "edge.452" successive ratio1 1 intervals 30 edge mesh "edge.441" "edge.4" successive ratio1 1 intervals 12 edge mesh "edge.462" "edge.434" successive ratio1 1 intervals 30 edge mesh "edge.435" "edge.436" successive ratio1 1 intervals 12 edge mesh "edge.5" "edge.3" successive ratio1 1 intervals 12 / volume mesh "volume.1" cooper source "face.71" "face.202" size 0.08 volume mesh "volume.36" cooper source "face.208" "face.214" size 0.08 / edge mesh "edge.468" successive ratio1 1 intervals 8 edge mesh "edge.2" "edge.467" "edge.7" successive ratio1 1 intervals 20 / face mesh "face.207" "face.217" "v_face.218" submap face mesh "v_face.219" submap volume mesh "v_volume.37" submap volume mesh "volume.35" map / / SPECIFYING CONTINUUM AND BOUNDARY TYPES / solver select "FIDAP" / physics create "fluid" ctype "FLUID" volume "v_volume.37" "volume.35" \ "volume.3" "volume.8" "volume.4" "volume.5" "volume.10" "volume.7" \ "volume.19" "volume.12" "volume.13" "volume.15" "volume.14" "volume.17" \ "volume.18" "volume.11" "volume.21" "volume.22" "volume.23" "volume.24" \ "volume.25" "volume.26" "volume.27" "volume.28" "volume.29" "volume.30" \ "volume.31" "volume.32" "volume.1" "volume.36" / physics create "tk_wall" btype "PLOT" face "face.3" physics create "tk_top" btype "PLOT" face "face.204" "face.4" "face.40" physics create "tk_bottom" btype "PLOT" face "face.2" "face.199" / physics create "tk_symm" btype "PLOT" face "face.71" "face.217" "face.208" \ "face.202" "face.207" "face.214" "v_face.219" "v_face.218" "face.44" \ "face.45" "face.52" "face.11" "face.96" "face.47" "face.90" "face.125" \
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Appendix D (Continued) 239 "face.131" "face.89" "face.137" "face.177" "face.113" "face.116" "face.106" \ "face.109" "face.111" "face.104" "face.85" "face.170" "face.79" "face.184" \ "face.149" "face.84" "face.121" "face.128" "face.38" / physics create "hp_sphr" btype "PLOT" face "face.10" "face.98" physics create "hp_cylr" btype "PLOT" face "face.6" physics create "hp_insu" btype "PLOT" face "face.46" / physics create "pp_outlet" btype "PLOT" face "face.18" "face.122" physics create "pp_inlet" btype "PLOT" face "face.28" "face.127" physics create "pp_pipe" btype "PLOT" face "face.86" "face.27" "face.140" physics create "pp_nozzle" btype "PLOT" face "face.147" "face.83" "face.17" \ "face.156" "face.155" "face.20" "face.13" physics create "pp_pump" btype "PLOT" face "face.176" "face.139" "face.180" \ "face.188" "face.25" "face.164" "face.148" "face.163" "face.153" "face.192" / / EXPORTING MESH / $ID = GETIDENT() $NEUTRALFILE = $ID + ".FDNEUT" export fidap $NEUTRALFILE D.2 Simulation Settings: FIDAP Commands / FIDAP Input File / SIMULATION SETTINGS / PROJECT: Cryogenic LH2 Tank with Lateral PumpNozzle Unit / Threedimensional (3D) model, SI units / / / F0: heat flux on tank wall, Fp: heat flux on pump wall / V0: nozzle speed, Tc: temperature of evaporator section of heat pipe $F0 = 2.0 $V0 = 0.01 $Tc = 18 $Fp = 0.01 / / CONVERSION OF NEUTRAL FILE TO FIDAP Database / FICONV( NEUTRAL ) INPUT( FILE="mesh.FDNEUT" ) OUTPUT( DELETE ) END /
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Appendix D (Continued) 240TITLE LH2 tank w/ heat pipe & lateral pumpnozzle unit / FIPREP / / PROBLEM SETUP / PROBLEM( 3D, TURBULENT, NONLINEAR, ENERGY ) EXECUTION( NEWJOB ) PRINTOUT( NONE ) DATAPRINT( NONE ) / / CONTINUUM ENTITIES / ENTITY ( NAME = "fluid", FLUID, PROPERTY = "fluid" ) / / BOUNDARY ENTITIES / ENTITY ( NAME = "tk_wall", WALL ) ENTITY ( NAME = "tk_top", WALL ) ENTITY ( NAME = "tk_bottom", WALL ) ENTITY ( NAME = "tk_symm", PLOT ) ENTITY ( NAME = "hp_sphr", WALL ) ENTITY ( NAME = "hp_cylr", WALL ) ENTITY ( NAME = "hp_insu", WALL ) ENTITY ( NAME = "pp_outlet", PLOT ) ENTITY ( NAME = "pp_inlet", PLOT ) ENTITY ( NAME = "pp_pipe", WALL ) ENTITY ( NAME = "pp_nozzle", WALL ) ENTITY ( NAME = "pp_pump", WALL ) / / SOLUTION PARAMETERS / SOLUTION( SEGREGATED = 100, VELCONV = .001 ) PRESSURE( MIXED = 1.E8, DISCONTINUOUS ) RELAX( HYBRID ) OPTIONS( UPWINDING ) / / MATERIAL PROPERTIES / / Partial list of Material Properties data / DENSITY( SET = "fluid", CONSTANT = 70.78 ) VISCOSITY( SET = "fluid", CONSTANT = 13.2E6, MIXLENGTH ) CONDUCTIVITY( SET = "fluid", CONSTANT = 0.099 ) SPECIFICHEAT( SET = "fluid", CONSTANT = 9.688E3 ) / / INITIAL AND BOUNDARY CONDITIONS / BCNODE( VELO, ZERO, ENTITY = "tk_wall" )
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Appendix D (Continued) 241BCNODE( VELO, ZERO, ENTITY = "tk_top" ) BCNODE( VELO, ZERO, ENTITY = "tk_bottom" ) BCNODE( UY, ZERO, ENTITY = "tk_symm" ) BCNODE( VELO, ZERO, ENTITY = "hp_sphr" ) BCNODE( VELO, ZERO, ENTITY = "hp_cylr" ) BCNODE( VELO, ZERO, ENTITY = "hp_insu" ) BCNODE( VELO, ZERO, ENTITY = "pp_pipe" ) BCNODE( VELO, ZERO, ENTITY = "pp_nozzle" ) BCNODE( VELO, ZERO, ENTITY = "pp_pump" ) / BCNODE( UX, ZERO, ENTITY = "pp_inlet" ) BCNODE( UY, ZERO, ENTITY = "pp_inlet" ) BCNODE( VELO, CONSTANT, ENTITY = "pp_outlet", X = $V0, Y = 0, Z = 0 ) BCNODE( TEMP, CONSTANT = $Tc, ENTITY = "hp_sphr" ) BCNODE( TEMP, CONSTANT = $Tc, ENTITY = "hp_cylr" ) BCFLUX( HEAT, CONSTANT = $Fp, ENTITY = "pp_pump" ) BCFLUX( HEAT, CONSTANT = $F0, ENTITY = "tk_wall" ) BCFLUX( HEAT, CONSTANT = $F0, ENTITY = "tk_top" ) BCFLUX( HEAT, CONSTANT = $F0, ENTITY = "tk_bottom" ) / CLIPPING( MINIMUM ) 0 0 0 0 $Tc / END / CREATE( FISOLV ) RUN( FISOLV, BACKGROUND )
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242 Appendix E: GAMBIT/FIDAP Preprocessing Input for Chapter 6 E.1 Geometry and Meshing: GAMBIT Commands / GAMBIT Input File / GEOMETRY and MESHING / PROJECT: Cryogenic LH2 Tank with Axial PumpNozzle Unit / Axisymmetric model, SI units / / CREATING THE GEOMETRY / vertex create coordinates 0 0 0 vertex create coordinates 0.65 0 0 vertex create coordinates 1.95 0 0 vertex create coordinates 2.6 0 0 vertex create coordinates 1.95 1.5 0 vertex create coordinates 0.65 1.5 0 edge create center "vertex.2" major "vertex.6" onedge "vertex.1" start 0 end \ 90 ellipse edge create center "vertex.3" major "vertex.5" onedge "vertex.4" start 0 end \ 90 ellipse edge create straight "vertex.6" "vertex.5" edge create straight "vertex.1" "vertex.4" vertex create coordinates 0 0.1 0 vertex create coordinates 1.2 0.1 0 vertex create coordinates 1.4 0.1 0 vertex create coordinates 1.4 0 0 vertex create coordinates 1.2 0 0 vertex create coordinates 1.5 0 0 coordinate create cartesian oldsystem "c_sys.1" offset 1.7 0 0 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation vertex create coordinates 0 0 0 vertex create coordinates 0 0.1 0 vertex create coordinates 0.05 0.1 0 vertex create coordinates 0.05 0.05 0 vertex create coordinates 0.1 0.05 0 vertex create coordinates 0.3 0 0 vertex create coordinates 0.6 0 0 vertex create coordinates 0.6 0.05 0 edge create center2points "vertex.16" "vertex.15" "vertex.17" minarc arc edge create straight "vertex.13" "vertex.14" "vertex.15" edge create straight "vertex.17" "vertex.20" "vertex.19" vertex create coordinates 0.3 0.1 0 vertex create coordinates 0.4 0 0 edge create center2points "vertex.18" "vertex.21" "vertex.22" circle edge split "edge.10" edge "edge.8" keeptool connected edge delete "edge.12" lowertopology edge split "edge.8" edge "edge.13" keeptool connected edge split "edge.15" edge "edge.10" keeptool connected
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Appendix E (Continued) 243edge delete "edge.15" lowertopology edge create straight "vertex.7" "vertex.8" "vertex.9" edge create center2points "vertex.10" "vertex.9" "vertex.12" minarc arc edge split "edge.1" edge "edge.18" keeptool connected edge delete "edge.22" lowertopology edge split "edge.18" edge "edge.1" keeptool connected edge delete "edge.18" lowertopology edge split "edge.4" edge "edge.20" keeptool connected edge delete "edge.4" lowertopology edge split "edge.24" edge "edge.6" keeptool connected edge split "edge.26" edge "edge.9" keeptool connected edge delete "edge.26" lowertopology face create wireframe "edge.1" "edge.3" "edge.2" "edge.28" "edge.9" "edge.17" \ "edge.10" "edge.13" "edge.8" "edge.5" "edge.7" "edge.6" "edge.24" \ "edge.20" "edge.19" "edge.22" real / / MESHING THE MODEL / blayer create first 0.005 growth 1.2 total 0.02684 rows 4 transition 1 trows \ 0 blayer attach "b_layer.1" face "face.1" "face.1" "face.1" "face.1" "face.1" \ "face.1" "face.1" "face.1" "face.1" "face.1" "face.1" "face.1" "face.1" \ "face.1" "face.1" "face.1" edge "edge.1" "edge.3" "edge.2" "edge.28" \ "edge.9" "edge.17" "edge.10" "edge.13" "edge.8" "edge.5" "edge.7" "edge.6" \ "edge.24" "edge.20" "edge.19" "edge.22" edge mesh "edge.19" "edge.20" "edge.24" successive ratio1 1 size 0.01 edge mesh "edge.6" "edge.9" successive ratio1 1 size 0.005 face mesh "face.1" pave size 0.02 / / SPECIFYING CONTINUUM AND BOUNDARY TYPES / solver select "FIDAP" / physics create "fluid" ctype "FLUID" face "face.1" physics create "tk_wall" btype "WALL" edge "edge.1" "edge.3" "edge.2" physics create "tk_symm" btype "PLOT" edge "edge.24" "edge.28" physics create "hp_adia" btype "WALL" edge "edge.22" physics create "hp_evap" btype "WALL" edge "edge.19" "edge.20" physics create "pp_wall" btype "WALL" edge "edge.7" "edge.5" "edge.8" \ "edge.13" "edge.10" "edge.17" physics create "pp_nozz" btype "PLOT" edge "edge.6" physics create "pp_suct" btype "PLOT" edge "edge.9" / / EXPORTING MESH /
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Appendix E (Continued) 244$ID = GETIDENT() $NEUTRALFILE = $ID + ".FDNEUT" export fidap $NEUTRALFILE E.2 Simulation Settings: FIDAP Commands / FIDAP Input File / SIMULATION SETTINGS STAGE 1 / PROJECT: Cryogenic LH2 Tank with Axial PumpNozzle Unit / Axisymmetric model, SI units, Transient analysis / / / F0: heat flux on tank wall / T1: temperature of evaporator section of heat pipe $F0 = 1 $T1 = 20 / FICONV( NEUTRAL ) INPUT( FILE="mesh.FDNEUT" ) OUTPUT( DELETE ) END / TITLE LH2 tank w/ heat pipe & axial pumpnozzle unit. Stage 1 / FIPREP / / PROBLEM SETUP / PROBLEM( AXI, TRANSIENT, TURBULENT, NONLINEAR, ENERGY ) EXECUTION( NEWJOB ) PRINTOUT( NONE ) DATAPRINT( NONE ) / / CONTINUUM ENTITIES / ENTITY ( NAME = "fluid", FLUID, PROPERTY = "fluid" ) / / BOUNDARY ENTITIES / ENTITY ( NAME = "tk_wall", WALL ) ENTITY ( NAME = "tk_symm", PLOT ) ENTITY ( NAME = "hp_adia", WALL ) ENTITY ( NAME = "hp_evap", WALL ) ENTITY ( NAME = "pp_wall", WALL ) ENTITY ( NAME = "pp_nozz", PLOT ) ENTITY ( NAME = "pp_suct", PLOT ) / / SOLUTION PARAMETERS / PRESSURE( PENALTY = 1.E9, DISCONTINUOUS )
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Appendix E (Continued) 245OPTIONS( UPWINDING ) SOLUTION( S.S. = 50, VELCONV = 1E4, RESCONV = 1E2, ACCF = 0.5 ) TIMEINTEGRATION( DT = 3600, NSTEPS = 84, FIXED ) / / MATERIAL PROPERTIES / / Partial list of Material Properties data / DENSITY( SET = "fluid", CONSTANT = 70 ) VISCOSITY( SET = "fluid", CONSTANT = 12E6, MIXLENGTH ) CONDUCTIVITY( SET = "fluid", CONSTANT = 0.1 ) SPECIFICHEAT( SET = "fluid", CONSTANT = 1E4 ) / / INITIAL AND BOUNDARY CONDITIONS / ICNODE( TEMP, CONSTANT = $T1, ALL ) / BCNODE( VELO, ZERO, ENTITY = "tk_wall" ) BCNODE( VELO, ZERO, ENTITY = "hp_adia" ) BCNODE( VELO, ZERO, ENTITY = "hp_evap" ) BCNODE( VELO, ZERO, ENTITY = "pp_wall" ) BCNODE( UY, ZERO, ENTITY = "tk_symm" ) BCNODE( VELO, ZERO, ENTITY = "pp_nozz" ) / BCFLUX( HEAT, CONSTANT = $F0, ENTITY = "tk_wall" ) BCNODE( TEMP, CONSTANT = $T1, ENTITY = "hp_evap" ) / CLIPPING( MINIMUM ) 0 0 0 0 $T1 END / CREATE( FISOLV ) RUN( FISOLV, BACKGROUND ) / FIDAP Input File / SIMULATION SETTINGS STAGE 2 / PROJECT: Cryogenic LH2 Tank with Axial PumpNozzle Unit / Axisymmetric model, SI units, Transient analysis / / / V2: fluid velocity at nozzle $V2 = 0.08 / TITLE LH2 tank w/ heat pipe & axial pumpnozzle unit. Stage 2 / FIPREP / / SOLUTION PARAMETERS / SOLUTION( S.S. = 50, VELCONV = 1E4, RESCONV = 1E2, ACCF = 0.5 ) TIMEINTEGRATION( DT = 300, NSTEPS = 12, FIXED )
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Appendix E (Continued) 246/ / INITIAL AND BOUNDARY CONDITIONS / ICNODE( TEMP, READ, ALL ) / BCNODE( UX, CONST = $V2, ENTITY = "pp_nozz" ) / END / CREATE( FISOLV ) RUN( FISOLV, BACKGROUND, RESTART = "stage1.FDPOST" ) / FIDAP Input File / SIMULATION SETTINGS STAGE 3 / PROJECT: Cryogenic LH2 Tank with Axial PumpNozzle Unit / Axisymmetric model, SI units, Transient analysis / / TITLE LH2 tank w/ heat pipe & axial pumpnozzle unit. Stage 3 / FIPREP / / SOLUTION PARAMETERS / SOLUTION( S.S. = 50, VELCONV = 1E4, RESCONV = 1E2, ACCF = 0.5 ) TIMEINTEGRATION( DT = 3600, NSTEPS = 67, FIXED ) / / INITIAL AND BOUNDARY CONDITIONS / ICNODE( TEMP, READ, ALL ) ICNODE( VELO, READ, ALL ) / BCNODE( UX, ZERO, ENTITY = "pp_nozz" ) BCNODE( VELO, ZERO, ENTITY = "pp_suct" ) / END / CREATE( FISOLV ) RUN( FISOLV, BACKGROUND, RESTART = "stage2.FDPOST" )
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247 Appendix F: GAMBIT/FIDAP Preprocessing Input for Chapter 7 F.1 Geometry and Meshing for 2D Model: GAMBIT Commands / GAMBIT Input File / GEOMETRY and MESHING / PROJECT: Refrigerated Warehouse with Ceiling Type Cooling Units / Twodimensional (2D) model, SI units / / / Neutral file name to be exported $ID = GETIDENT() $NEUTRALFILE = $ID + ".FDNEUT" / / Boundary layer mesh parameters: R = ratio, N = number of intervals $R = 1.5 $N = 3 $S = 0.1 / / Evaporator position index $I = 0 $J = 0 / / $J /  Simulation #  Position  $I  $J   / 384 /  0  CENTER  0  0     /  1  SW  1  1     /  2  SE  +1  1  607$I /  3  NW  1  +1     /  4  NE  +1  +1     / 152 /  5  S  0  1  /  6  W  1  0  /  7  E  +1  0  /  8  N  0  +1  / / / X = distance from front wall to evaporator face / Y = height of evaporator (fan) centerline $X0 = 1.1 $Y0 = 3.3 $dX = 0.2 $dY = 0.2 $X = $X0 + $dX*$I $Y = $Y0 + $dY*$J / / REFRIGERATED SPACE / face create width 7.0 height 4.0 offset 3.5 2.0 0 xyplane rectangle face create width 6.9 height 3.9 offset 3.5 2.0 0 xyplane rectangle edge create straight "vertex.1" "vertex.5" edge create straight "vertex.2" "vertex.6"
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Appendix F (Continued) 248edge create straight "vertex.3" "vertex.7" edge create straight "vertex.4" "vertex.8" face create wireframe "edge.1" "edge.5" "edge.9" "edge.10" real face create wireframe "edge.2" "edge.6" "edge.10" "edge.11" real face create wireframe "edge.3" "edge.7" "edge.11" "edge.12" real face create wireframe "edge.4" "edge.8" "edge.12" "edge.9" real / / PACKAGES / coordinate create cartesian oldsystem "c_sys.1" offset 1.7 0.1 0 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation face create width 1.2 height 0.8 offset 0.6 0.4 0 xyplane rectangle face create width 1.3 height 0.9 offset 0.6 0.4 0 xyplane rectangle face cmove "face.7" "face.8" multiple 2 offset 0 0.9 0 face cmove "face.7" "face.8" "face.9" "face.10" "face.11" "face.12" \ multiple 3 offset 1.3 0 0 / face split "face.2" connected face "face.8" face split "face.2" connected face "face.10" face split "face.2" connected face "face.12" face split "face.2" connected face "face.14" face split "face.2" connected face "face.16" face split "face.2" connected face "face.18" face split "face.2" connected face "face.20" face split "face.2" connected face "face.22" face split "face.2" connected face "face.24" face split "face.2" connected face "face.26" face split "face.2" connected face "face.28" face split "face.2" connected face "face.30" / / 1 edge create straight "vertex.9" "vertex.105" edge create straight "vertex.10" "vertex.106" edge create straight "vertex.11" "vertex.108" edge create straight "vertex.12" "vertex.107" / 2 edge create straight "vertex.17" "vertex.107" edge create straight "vertex.18" "vertex.108" edge create straight "vertex.19" "vertex.110" edge create straight "vertex.20" "vertex.109" / 3 edge create straight "vertex.25" "vertex.109" edge create straight "vertex.26" "vertex.110" edge create straight "vertex.27" "vertex.112" edge create straight "vertex.28" "vertex.111" / 4 edge create straight "vertex.33" "vertex.106" edge create straight "vertex.34" "vertex.113" edge create straight "vertex.35" "vertex.114" edge create straight "vertex.36" "vertex.108" / 5 edge create straight "vertex.41" "vertex.108"
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Appendix F (Continued) 249edge create straight "vertex.42" "vertex.114" edge create straight "vertex.43" "vertex.115" edge create straight "vertex.44" "vertex.110" / 6 edge create straight "vertex.49" "vertex.110" edge create straight "vertex.50" "vertex.115" edge create straight "vertex.51" "vertex.116" edge create straight "vertex.52" "vertex.112" / 7 edge create straight "vertex.57" "vertex.113" edge create straight "vertex.58" "vertex.117" edge create straight "vertex.59" "vertex.118" edge create straight "vertex.60" "vertex.114" / 8 edge create straight "vertex.65" "vertex.114" edge create straight "vertex.66" "vertex.118" edge create straight "vertex.67" "vertex.119" edge create straight "vertex.68" "vertex.115" / 9 edge create straight "vertex.73" "vertex.115" edge create straight "vertex.74" "vertex.119" edge create straight "vertex.75" "vertex.120" edge create straight "vertex.76" "vertex.116" / 10 edge create straight "vertex.81" "vertex.117" edge create straight "vertex.82" "vertex.121" edge create straight "vertex.83" "vertex.122" edge create straight "vertex.84" "vertex.118" / 11 edge create straight "vertex.89" "vertex.118" edge create straight "vertex.90" "vertex.122" edge create straight "vertex.91" "vertex.123" edge create straight "vertex.92" "vertex.119" / 12 edge create straight "vertex.97" "vertex.119" edge create straight "vertex.98" "vertex.123" edge create straight "vertex.99" "vertex.124" edge create straight "vertex.100" "vertex.120" / / 1 face create wireframe "edge.13" "edge.109" "edge.141" "edge.142" real face create wireframe "edge.14" "edge.112" "edge.142" "edge.143" real face create wireframe "edge.15" "edge.113" "edge.143" "edge.144" real face create wireframe "edge.16" "edge.111" "edge.144" "edge.141" real / 2 face create wireframe "edge.21" "edge.113" "edge.145" "edge.146" real face create wireframe "edge.22" "edge.115" "edge.146" "edge.147" real face create wireframe "edge.23" "edge.116" "edge.147" "edge.148" real face create wireframe "edge.24" "edge.114" "edge.148" "edge.145" real / 3 face create wireframe "edge.29" "edge.116" "edge.149" "edge.150" real face create wireframe "edge.30" "edge.118" "edge.150" "edge.151" real face create wireframe "edge.31" "edge.119" "edge.151" "edge.152" real
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Appendix F (Continued) 250face create wireframe "edge.32" "edge.117" "edge.152" "edge.149" real / 4 face create wireframe "edge.37" "edge.110" "edge.153" "edge.154" real face create wireframe "edge.38" "edge.121" "edge.154" "edge.155" real face create wireframe "edge.39" "edge.122" "edge.155" "edge.156" real face create wireframe "edge.40" "edge.112" "edge.156" "edge.153" real / 5 face create wireframe "edge.45" "edge.122" "edge.157" "edge.158" real face create wireframe "edge.46" "edge.123" "edge.158" "edge.159" real face create wireframe "edge.47" "edge.124" "edge.159" "edge.160" real face create wireframe "edge.48" "edge.115" "edge.160" "edge.157" real / 6 face create wireframe "edge.53" "edge.124" "edge.161" "edge.162" real face create wireframe "edge.54" "edge.125" "edge.162" "edge.163" real face create wireframe "edge.55" "edge.126" "edge.163" "edge.164" real face create wireframe "edge.56" "edge.118" "edge.164" "edge.161" real / 7 face create wireframe "edge.61" "edge.120" "edge.165" "edge.166" real face create wireframe "edge.62" "edge.128" "edge.166" "edge.167" real face create wireframe "edge.63" "edge.129" "edge.167" "edge.168" real face create wireframe "edge.64" "edge.121" "edge.168" "edge.165" real / 8 face create wireframe "edge.69" "edge.129" "edge.169" "edge.170" real face create wireframe "edge.70" "edge.130" "edge.170" "edge.171" real face create wireframe "edge.71" "edge.131" "edge.171" "edge.172" real face create wireframe "edge.72" "edge.123" "edge.172" "edge.169" real / 9 face create wireframe "edge.77" "edge.131" "edge.173" "edge.174" real face create wireframe "edge.78" "edge.132" "edge.174" "edge.175" real face create wireframe "edge.79" "edge.133" "edge.175" "edge.176" real face create wireframe "edge.80" "edge.125" "edge.176" "edge.173" real / 10 face create wireframe "edge.85" "edge.127" "edge.177" "edge.178" real face create wireframe "edge.86" "edge.135" "edge.178" "edge.179" real face create wireframe "edge.87" "edge.136" "edge.179" "edge.180" real face create wireframe "edge.88" "edge.128" "edge.180" "edge.177" real / 11 face create wireframe "edge.93" "edge.136" "edge.181" "edge.182" real face create wireframe "edge.94" "edge.137" "edge.182" "edge.183" real face create wireframe "edge.95" "edge.138" "edge.183" "edge.184" real face create wireframe "edge.96" "edge.130" "edge.184" "edge.181" real / 12 face create wireframe "edge.101" "edge.138" "edge.185" "edge.186" real face create wireframe "edge.102" "edge.139" "edge.186" "edge.187" real face create wireframe "edge.103" "edge.140" "edge.187" "edge.188" real face create wireframe "edge.104" "edge.132" "edge.188" "edge.185" real / / EVAPORATOR /
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Appendix F (Continued) 251coordinate create cartesian oldsystem "c_sys.1" offset $X $Y 0 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation face create width 0.4 height 0.6 offset 0.2 0 0 xyplane rectangle face create width 0.5 height 0.7 offset 0.2 0 0 xyplane rectangle face create width 0.5 height 0.4 offset 0.2 0 0 xyplane rectangle vertex create coordinates 0.05 0 0 vertex create coordinates 0.2 0 0 face create center "vertex.137" major "vertex.135" onedge "vertex.138" ellipse face creflect "face.94" multiple 1 vector 1 0 0 origin 0.2 0 0 face create width 0.9 height 0.06 offset 0.2 0 0 xyplane rectangle face create width 0.9 height 0.5 offset 0.2 0 0 xyplane rectangle face unite faces "face.93" "face.94" "face.95" real face create width 8 height 0.2 offset 0.25 0 0 yzplane rectangle face split "face.2" face "face.98" face split "face.99" connected face "face.91" face split "face.99" connected face "face.93" face split "face.99" connected face "face.92" face split "face.99" connected face "face.97" bientity face delete "face.97" lowertopology face split "face.101" connected face "face.96" keeptool face split "face.93" connected face "face.96" / / MESHING / default set "MESH.NODES.EDGE" numeric 2 default set "MESH.NODES.QUAD" numeric 4 / / MESH UNOCCUPIED SPACE / face mesh "face.2" "face.99" submap size $S / / MESH PACKAGE ENVELOPES / edge mesh "edge.141" "edge.142" "edge.143" "edge.144" "edge.145" \ "edge.146" "edge.147" "edge.148" "edge.149" "edge.150" \ "edge.151" "edge.152" "edge.153" "edge.154" "edge.155" \ "edge.156" "edge.157" "edge.158" "edge.159" "edge.160" \ "edge.161" "edge.162" "edge.163" "edge.164" "edge.165" \ "edge.166" "edge.167" "edge.168" "edge.169" "edge.170" \ "edge.171" "edge.172" "edge.173" "edge.174" "edge.175" \ "edge.176" "edge.177" "edge.178" "edge.179" "edge.180" \ "edge.181" "edge.182" "edge.183" "edge.184" "edge.185" \ "edge.186" "edge.187" "edge.188" \ successive ratio1 $R intervals $N face mesh "face.43" "face.44" "face.45" "face.46" "face.47" "face.48" \ "face.49" "face.50" "face.51" "face.52" "face.53" "face.54" "face.55" \ "face.56" "face.57" "face.58" "face.59" "face.60" "face.61" "face.62" \
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Appendix F (Continued) 252 "face.63" "face.64" "face.65" "face.66" "face.67" "face.68" "face.69" \ "face.70" "face.71" "face.72" "face.73" "face.74" "face.75" "face.76" \ "face.77" "face.78" "face.79" "face.80" "face.81" "face.82" "face.83" \ "face.84" "face.85" "face.86" "face.87" "face.88" "face.89" "face.90" \ map size $S / / MESH PACKAGES / face mesh "face.7" "face.9" "face.11" "face.13" "face.15" "face.17" "face.19" \ "face.21" "face.23" "face.25" "face.27" "face.29" map / / MESH FLOOR, WALLS, CEILING / edge mesh "edge.9" "edge.10" "edge.11" "edge.12" \ successive ratio1 $R intervals $N face mesh "face.3" "face.4" "face.5" "face.6" map / / MESH EVAPORATOR, INLET/OUTLET / edge mesh "edge.234" "edge.235" "edge.242" "edge.243" successive ratio1 1 \ intervals 2 edge mesh "edge.219" "edge.220" "edge.222" "edge.231" successive ratio1 1 \ intervals 3 edge modify "edge.224" "edge.229" backward edge mesh "edge.223" "edge.224" "edge.229" "edge.230" successive ratio1 $R \ intervals $N edge modify "edge.252" "edge.261" backward edge mesh "edge.252" "edge.227" "edge.261" "edge.226" firstlength ratio1 \ 0.025 intervals 4 / face modify "face.103" side "vertex.166" face modify "face.103" side "vertex.167" face modify "face.103" side "vertex.154" face modify "face.103" side "vertex.155" face mesh "face.103" map face modify "face.92" side "vertex.168" face modify "face.92" side "vertex.169" face modify "face.92" side "vertex.156" face modify "face.92" side "vertex.157" face mesh "face.92" map face modify "face.105" side "vertex.145" face modify "face.105" side "vertex.146" face mesh "face.105" map face mesh "face.101" "face.108" triprimitive
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Appendix F (Continued) 253face mesh "face.107" map face modify "face.106" side "vertex.144" face modify "face.106" side "vertex.147" face mesh "face.106" map face mesh "face.93" "face.110" triprimitive face mesh "face.96" map / / DEFINING ENTITIES / solver select "FIDAP" physics create "floor" btype "WALL" edge "edge.1" physics create "ceiling" btype "WALL" edge "edge.3" physics create "wall_1" btype "WALL" edge "edge.4" physics create "wall_2" btype "WALL" edge "edge.2" / physics create "box_11" btype "WALL" edge "edge.13" "edge.14" "edge.15" \ "edge.16" physics create "box_21" btype "WALL" edge "edge.21" "edge.22" "edge.23" \ "edge.24" physics create "box_31" btype "WALL" edge "edge.29" "edge.30" "edge.31" \ "edge.32" physics create "box_12" btype "WALL" edge "edge.37" "edge.38" "edge.39" \ "edge.40" physics create "box_22" btype "WALL" edge "edge.45" "edge.46" "edge.47" \ "edge.48" physics create "box_32" btype "WALL" edge "edge.53" "edge.54" "edge.55" \ "edge.56" physics create "box_13" btype "WALL" edge "edge.61" "edge.62" "edge.63" \ "edge.64" physics create "box_23" btype "WALL" edge "edge.69" "edge.70" "edge.71" \ "edge.72" physics create "box_33" btype "WALL" edge "edge.77" "edge.78" "edge.79" \ "edge.80" physics create "box_14" btype "WALL" edge "edge.85" "edge.86" "edge.87" \ "edge.88" physics create "box_24" btype "WALL" edge "edge.93" "edge.94" "edge.95" \ "edge.96" physics create "box_34" btype "WALL" edge "edge.101" "edge.102" "edge.103" \ "edge.104" / physics create "evap_cover" btype "WALL" edge "edge.219" "edge.218" \
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Appendix F (Continued) 254 "edge.222" "edge.220" "edge.221" "edge.231" physics create "evap_blow" btype "PLOT" edge "edge.227" "edge.252" \ "edge.254" physics create "evap_suct" btype "PLOT" edge "edge.226" "edge.259" \ "edge.261" / physics create "fluid" ctype "FLUID" face \ "face.2" "face.99" "face.3" "face.4" "face.5" "face.6" \ "face.43" "face.44" "face.45" "face.46" "face.47" "face.48" \ "face.49" "face.50" "face.51" "face.52" "face.53" "face.54" "face.55" \ "face.56" "face.57" "face.58" "face.59" "face.60" "face.61" "face.62" \ "face.63" "face.64" "face.65" "face.66" "face.67" "face.68" "face.69" \ "face.70" "face.71" "face.72" "face.73" "face.74" "face.75" "face.76" \ "face.77" "face.78" "face.79" "face.80" "face.81" "face.82" "face.83" \ "face.84" "face.85" "face.86" "face.87" "face.88" "face.89" "face.90" \ "face.103" "face.92" "face.105" "face.106" "face.107" "face.101" \ "face.108" "face.96" "face.93" "face.110" physics create "pack_11" ctype "SOLID" face "face.7" physics create "pack_21" ctype "SOLID" face "face.9" physics create "pack_31" ctype "SOLID" face "face.11" physics create "pack_12" ctype "SOLID" face "face.13" physics create "pack_22" ctype "SOLID" face "face.15" physics create "pack_32" ctype "SOLID" face "face.17" physics create "pack_13" ctype "SOLID" face "face.19" physics create "pack_23" ctype "SOLID" face "face.21" physics create "pack_33" ctype "SOLID" face "face.23" physics create "pack_14" ctype "SOLID" face "face.25" physics create "pack_24" ctype "SOLID" face "face.27" physics create "pack_34" ctype "SOLID" face "face.29" / export fidap $NEUTRALFILE F.2 Simulation Settings for 2D Model: FIDAP Commands / FIDAP Input File / SIMULATION SETTINGS / PROJECT: Refrigerated Warehouse with Ceiling Type Cooling Units / Twodimensional (2D) model, SI units / / / Neutral file name $NEUTRALFILE = "mesh.FDNEUT" / / CONVERSION OF NEUTRAL FILE TO FIDAP Database /
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Appendix F (Continued) 255FICONV( NEUTRAL ) INPUT( FILE=$NEUTRALFILE ) OUTPUT( DELETE ) END / TITLE Refrigerated Warehouse, 2D model / / CONSTANTS / $V_SUPPLY = 0.5 $T_SUPPLY = 0 $F_LIGHT = 10 / IF ( $T_SUPPLY .EQ. 0 ) $T_MIN = 1.E20 ELSE $T_MIN = $T_SUPPLY ENDIF / $G = 9.8 $RHO = 1.293 $MU = 17.20E6 $K = 24.07E3 $CP = 1.004E3 $BETA = 3.663E3 $TREF = 0 / $RHO_2 = 840 $K_2 = 0.52 $CP_2 = 3.79E3 / $H_CCF = 1.18 $T_GROUND = 15 $H_PUR = 0.23 $T_AMBIENT = 35 $T_LIGHTEQ = $T_AMBIENT + $F_LIGHT/$H_PUR / / ABBREVIATIONS / CCF: concrete floor / PUR: polyurethane / FIPREP / / PROBLEM SETUP / GRAVITY( MAGNITUDE = $G ) PROBLEM( 2D, TURBULENT, NONLINEAR, BUOYANCY ) EXECUTION( NEWJOB ) PRINTOUT( NONE ) DATAPRINT( NONE ) / / CONTINUUM ENTITIES
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Appendix F (Continued) 256/ ENTITY( NAME = "fluid", FLUID, PROPERTY = "fluid" ) ENTITY( NAME = "pack_11", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_21", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_31", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_12", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_22", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_32", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_13", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_23", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_33", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_14", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_24", SOLID, PROPERTY = "pack" ) ENTITY( NAME = "pack_34", SOLID, PROPERTY = "pack" ) / / BOUNDARY ENTITIES / ENTITY( NAME = "floor", CONVECTION, MCNV = "floor" ) ENTITY( NAME = "ceiling", CONVECTION, MCNV = "light" ) ENTITY( NAME = "wall_1", CONVECTION, MCNV = "walls" ) ENTITY( NAME = "wall_2", CONVECTION, MCNV = "walls" ) ENTITY( NAME = "box_11", WALL, ATTACH = "fluid", NATTACH = "pack_11") ENTITY( NAME = "box_21", WALL, ATTACH = "fluid", NATTACH = "pack_21") ENTITY( NAME = "box_31", WALL, ATTACH = "fluid", NATTACH = "pack_31") ENTITY( NAME = "box_12", WALL, ATTACH = "fluid", NATTACH = "pack_12") ENTITY( NAME = "box_22", WALL, ATTACH = "fluid", NATTACH = "pack_22") ENTITY( NAME = "box_32", WALL, ATTACH = "fluid", NATTACH = "pack_32") ENTITY( NAME = "box_13", WALL, ATTACH = "fluid", NATTACH = "pack_13") ENTITY( NAME = "box_23", WALL, ATTACH = "fluid", NATTACH = "pack_23") ENTITY( NAME = "box_33", WALL, ATTACH = "fluid", NATTACH = "pack_33") ENTITY( NAME = "box_14", WALL, ATTACH = "fluid", NATTACH = "pack_14") ENTITY( NAME = "box_24", WALL, ATTACH = "fluid", NATTACH = "pack_24") ENTITY( NAME = "box_34", WALL, ATTACH = "fluid", NATTACH = "pack_34") ENTITY( NAME = "evap_cover", WALL ) ENTITY( NAME = "evap_blow", PLOT ) ENTITY( NAME = "evap_suct", PLOT ) / / SOLUTION PARAMETERS / SOLUTION( S.S. = 100, VELCONV = .01, RESCONV = .01, ACCF = .5 ) PRESSURE( MIXED = 1.E9, DISCONTINUOUS ) OPTIONS( UPWINDING ) POSTPROCESS( RESIDUAL ) CLIPPING( MINIMUM ) 0 0 0 0 $T_MIN / / MATERIAL PROPERTIES / / Partial list of Material Properties data / DENSITY( SET = "fluid", CONSTANT = $RHO ) VISCOSITY( SET = "fluid", CONSTANT = $MU, MIXLENGTH ) CONDUCTIVITY( SET = "fluid", CONSTANT = $K )
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Appendix F (Continued) 257SPECIFICHEAT( SET = "fluid", CONSTANT = $CP ) VOLUMEXPANSION( SET = "fluid", CONSTANT = $BETA, REFTEMP = $TREF ) / DENSITY( SET = "pack", CONSTANT = $RHO_2 ) CONDUCTIVITY( SET = "pack", CONSTANT = $K_2 ) SPECIFICHEAT( SET = "pack", CONSTANT = $CP_2 ) / HTRANSFER( SET = "floor", CONSTANT = $H_CCF, REFTEMP = $T_GROUND ) HTRANSFER( SET = "light", CONSTANT = $H_PUR, REFTEMP = $T_LIGHTEQ ) HTRANSFER( SET = "walls", CONSTANT = $H_PUR, REFTEMP = $T_AMBIENT ) / / INITIAL AND BOUNDARY CONDITIONS / BCNODE( VELO, ZERO, ENTITY = "floor" ) BCNODE( VELO, ZERO, ENTITY = "ceiling" ) BCNODE( VELO, ZERO, ENTITY = "wall_1" ) BCNODE( VELO, ZERO, ENTITY = "wall_2" ) BCNODE( VELO, ZERO, ENTITY = "box_11" ) BCNODE( VELO, ZERO, ENTITY = "box_21" ) BCNODE( VELO, ZERO, ENTITY = "box_31" ) BCNODE( VELO, ZERO, ENTITY = "box_12" ) BCNODE( VELO, ZERO, ENTITY = "box_22" ) BCNODE( VELO, ZERO, ENTITY = "box_32" ) BCNODE( VELO, ZERO, ENTITY = "box_13" ) BCNODE( VELO, ZERO, ENTITY = "box_23" ) BCNODE( VELO, ZERO, ENTITY = "box_33" ) BCNODE( VELO, ZERO, ENTITY = "box_14" ) BCNODE( VELO, ZERO, ENTITY = "box_24" ) BCNODE( VELO, ZERO, ENTITY = "box_34" ) BCNODE( VELO, ZERO, ENTITY = "evap_cover" ) BCNODE( VELO, CONSTANT, X = $V_SUPPLY, Y = 0, Z = 0, ENTITY = "evap_blow" ) / BCNODE( TEMP, CONSTANT = $T_SUPPLY, ENTITY = "evap_blow" ) / END / CREATE( FISOLV ) RUN( FISOLV, BACKGROUND ) F.3 Geometry and Meshing for 3D Model: GAMBIT Commands / GAMBIT Input File / GEOMETRY and MESHING / PROJECT: Refrigerated Warehouse with Ceiling Type Cooling Units / Threedimensional (3D) model, SI units / / / Mesh parameters (based on boundary layer thickness of 0.05 m) / $S = regular mesh size / $R = successive ratio (mesh edges)/growth factor (boundary layers)
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Appendix F (Continued) 258/ $F = firstrow height (boundary layers) / $N = number of rows (boundary layers) / $B = total thickness of boundary layer / $S = 0.1 $B = 0.05 $N = 3 $R = 1.5 $F = $B/(1+$R+$R*$R) $M = $N + 2 / / Evaporator position index $I = 1 $J = 0 / / $J /  Simulation #  Position  $I  $J   / 384 /  0  CENTER  0  0     /  1  SW  1  1     /  2  SE  +1  1  607$I /  3  NW  1  +1     /  4  NE  +1  +1     / 152 /  5  S  0  1  /  6  W  1  0  /  7  E  +1  0  /  8  N  0  +1  / / / W = distance from front wall to evaporator face / H = height of evaporator (fan) centerline / $W0 = 1.1 $H0 = 3.3 $dW = 0.2 $dH = 0.2 $W = $W0 + $dW*$I $H = $H0 + $dH*$J / / REFRIGERATED SPACE / volume create width 7 depth 2 height 4 offset 3.5 1 2 brick volume create width 6.9 depth 2 height 3.9 offset 3.5 1 2 brick edge create straight "vertex.1" "vertex.9" edge create straight "vertex.2" "vertex.10" edge create straight "vertex.3" "vertex.11" edge create straight "vertex.4" "vertex.12" edge create straight "vertex.5" "vertex.13" edge create straight "vertex.6" "vertex.14" edge create straight "vertex.7" "vertex.15" edge create straight "vertex.8" "vertex.16"
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Appendix F (Continued) 259volume create wireframe "edge.1" "edge.2" "edge.3" "edge.4" "edge.25" \ "edge.26" "edge.27" "edge.28" "edge.13" "edge.14" "edge.15" "edge.16" volume create wireframe "edge.2" "edge.5" "edge.7" "edge.10" "edge.25" \ "edge.27" "edge.29" "edge.31" "edge.14" "edge.17" "edge.22" "edge.19" volume create wireframe "edge.3" "edge.6" "edge.8" "edge.11" "edge.26" \ "edge.28" "edge.30" "edge.32" "edge.15" "edge.18" "edge.20" "edge.23" volume create wireframe "edge.9" "edge.10" "edge.11" "edge.12" "edge.29" \ "edge.30" "edge.31" "edge.32" "edge.21" "edge.22" "edge.23" "edge.24" volume delete "volume.1" lowertopology / / PACKAGES / coordinate create cartesian oldsystem "c_sys.1" offset 1.7 0 0.1 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width 1.2 depth 0.95 height 0.8 offset 0.6 0.475 0.4 brick volume create width 1.3 depth 1.05 height 0.9 offset 0.6 0.475 0.4 brick volume cmove "volume.7" "volume.8" multiple 2 offset 0 0 0.9 volume cmove "volume.7" "volume.8" "volume.9" "volume.10" "volume.11" \ "volume.12" multiple 3 offset 1.3 0 0 / volume split "volume.2" volumes "volume.8" connected volume split "volume.2" volumes "volume.10" connected volume split "volume.2" volumes "volume.12" connected volume split "volume.2" volumes "volume.14" connected volume split "volume.2" volumes "volume.16" connected volume split "volume.2" volumes "volume.18" connected volume split "volume.2" volumes "volume.20" connected volume split "volume.2" volumes "volume.22" connected volume split "volume.2" volumes "volume.24" connected volume split "volume.2" volumes "volume.26" connected volume split "volume.2" volumes "volume.28" connected volume split "volume.2" volumes "volume.30" connected / 1 edge create straight "vertex.17" "vertex.209" edge create straight "vertex.18" "vertex.210" edge create straight "vertex.19" "vertex.211" edge create straight "vertex.20" "vertex.212" edge create straight "vertex.21" "vertex.213" edge create straight "vertex.22" "vertex.214" edge create straight "vertex.23" "vertex.31" edge create straight "vertex.24" "vertex.32"
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Appendix F (Continued) 260volume create wireframe "edge.33" "edge.34" "edge.35" "edge.36" "edge.374" \ "edge.375" "edge.376" "edge.377" "edge.322" "edge.323" "edge.324" \ "edge.325" volume create wireframe "edge.34" "edge.37" "edge.39" "edge.42" "edge.374" \ "edge.376" "edge.378" "edge.380" "edge.323" "edge.326" "edge.51" "edge.54" volume create wireframe "edge.35" "edge.38" "edge.40" "edge.43" "edge.375" \ "edge.377" "edge.379" "edge.381" "edge.324" "edge.327" "edge.52" "edge.329" volume create wireframe "edge.41" "edge.42" "edge.43" "edge.44" "edge.378" \ "edge.379" "edge.380" "edge.381" "edge.328" "edge.54" "edge.329" "edge.56" volume create wireframe "edge.36" "edge.39" "edge.40" "edge.44" "edge.376" \ "edge.377" "edge.380" "edge.381" "edge.325" "edge.51" "edge.52" "edge.56" / 2 edge create straight "vertex.39" "vertex.213" edge create straight "vertex.38" "vertex.214" edge create straight "vertex.40" "vertex.31" edge create straight "vertex.37" "vertex.32" edge create straight "vertex.36" "vertex.215" edge create straight "vertex.33" "vertex.216" edge create straight "vertex.35" "vertex.43" edge create straight "vertex.34" "vertex.42" volume create wireframe "edge.62" "edge.63" "edge.61" "edge.64" "edge.382" \ "edge.383" "edge.384" "edge.385" "edge.328" "edge.54" "edge.329" "edge.56" volume create wireframe "edge.63" "edge.65" "edge.67" "edge.59" "edge.382" \ "edge.384" "edge.386" "edge.388" "edge.54" "edge.330" "edge.79" "edge.71" volume create wireframe "edge.61" "edge.66" "edge.68" "edge.57" "edge.383" \ "edge.385" "edge.387" "edge.389" "edge.329" "edge.331" "edge.80" "edge.333" volume create wireframe "edge.60" "edge.59" "edge.57" "edge.58" "edge.386" \ "edge.387" "edge.388" "edge.389" "edge.332" "edge.71" "edge.333" "edge.70" volume create wireframe "edge.64" "edge.67" "edge.68" "edge.58" "edge.384" \ "edge.385" "edge.388" "edge.389" "edge.56" "edge.79" "edge.80" "edge.70" / 3 edge create straight "vertex.55" "vertex.215" edge create straight "vertex.54" "vertex.216" edge create straight "vertex.56" "vertex.43"
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Appendix F (Continued) 261edge create straight "vertex.53" "vertex.42" edge create straight "vertex.52" "vertex.217" edge create straight "vertex.49" "vertex.218" edge create straight "vertex.51" "vertex.59" edge create straight "vertex.50" "vertex.58" volume create wireframe "edge.86" "edge.87" "edge.85" "edge.88" "edge.390" \ "edge.391" "edge.392" "edge.393" "edge.332" "edge.71" "edge.333" "edge.70" volume create wireframe "edge.87" "edge.89" "edge.91" "edge.83" "edge.390" \ "edge.392" "edge.394" "edge.396" "edge.71" "edge.334" "edge.103" "edge.95" volume create wireframe "edge.85" "edge.90" "edge.92" "edge.81" "edge.391" \ "edge.393" "edge.395" "edge.397" "edge.333" "edge.335" "edge.104" \ "edge.337" volume create wireframe "edge.84" "edge.83" "edge.81" "edge.82" "edge.394" \ "edge.395" "edge.396" "edge.397" "edge.336" "edge.95" "edge.337" "edge.94" volume create wireframe "edge.88" "edge.91" "edge.92" "edge.82" "edge.392" \ "edge.393" "edge.396" "edge.397" "edge.70" "edge.103" "edge.104" "edge.94" / 4 edge create straight "vertex.71" "vertex.210" edge create straight "vertex.70" "vertex.219" edge create straight "vertex.72" "vertex.212" edge create straight "vertex.69" "vertex.220" edge create straight "vertex.68" "vertex.214" edge create straight "vertex.65" "vertex.221" edge create straight "vertex.67" "vertex.32" edge create straight "vertex.66" "vertex.74" volume create wireframe "edge.110" "edge.111" "edge.109" "edge.112" \ "edge.398" "edge.399" "edge.400" "edge.401" "edge.338" "edge.324" \ "edge.339" "edge.340" volume create wireframe "edge.111" "edge.113" "edge.115" "edge.107" \ "edge.398" "edge.400" "edge.402" "edge.404" "edge.324" "edge.327" "edge.52" \ "edge.329" volume create wireframe "edge.109" "edge.114" "edge.116" "edge.105" \ "edge.399" "edge.401" "edge.403" "edge.405" "edge.339" "edge.341" \ "edge.128" "edge.343" volume create wireframe "edge.108" "edge.107" "edge.105" "edge.106" \ "edge.402" "edge.403" "edge.404" "edge.405" "edge.342" "edge.329" \ "edge.343" "edge.118" volume create wireframe "edge.112" "edge.115" "edge.116" "edge.106" \ "edge.400" "edge.401" "edge.404" "edge.405" "edge.340" "edge.52" "edge.128" \ "edge.118" / 5 edge create straight "vertex.87" "vertex.214"
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Appendix F (Continued) 262edge create straight "vertex.86" "vertex.221" edge create straight "vertex.88" "vertex.32" edge create straight "vertex.85" "vertex.74" edge create straight "vertex.84" "vertex.216" edge create straight "vertex.81" "vertex.222" edge create straight "vertex.83" "vertex.42" edge create straight "vertex.82" "vertex.90" volume create wireframe "edge.134" "edge.135" "edge.133" "edge.136" \ "edge.406" "edge.407" "edge.408" "edge.409" "edge.342" "edge.329" \ "edge.343" "edge.118" volume create wireframe "edge.135" "edge.137" "edge.139" "edge.131" \ "edge.406" "edge.408" "edge.410" "edge.412" "edge.329" "edge.331" "edge.80" \ "edge.333" volume create wireframe "edge.133" "edge.138" "edge.140" "edge.129" \ "edge.407" "edge.409" "edge.411" "edge.413" "edge.343" "edge.344" \ "edge.152" "edge.346" volume create wireframe "edge.132" "edge.131" "edge.129" "edge.130" \ "edge.411" "edge.410" "edge.412" "edge.413" "edge.345" "edge.333" \ "edge.346" "edge.142" volume create wireframe "edge.136" "edge.139" "edge.140" "edge.130" \ "edge.408" "edge.409" "edge.412" "edge.413" "edge.118" "edge.80" "edge.152" \ "edge.142" / 6 edge create straight "vertex.103" "vertex.216" edge create straight "vertex.102" "vertex.222" edge create straight "vertex.104" "vertex.42" edge create straight "vertex.101" "vertex.90" edge create straight "vertex.100" "vertex.218" edge create straight "vertex.97" "vertex.223" edge create straight "vertex.99" "vertex.58" edge create straight "vertex.98" "vertex.106" volume create wireframe "edge.158" "edge.159" "edge.157" "edge.160" \ "edge.414" "edge.415" "edge.416" "edge.417" "edge.345" "edge.333" \ "edge.346" "edge.142" volume create wireframe "edge.159" "edge.161" "edge.163" "edge.155" \ "edge.414" "edge.416" "edge.418" "edge.420" "edge.333" "edge.335" \ "edge.104" "edge.337" volume create wireframe "edge.157" "edge.162" "edge.164" "edge.153" \ "edge.415" "edge.417" "edge.419" "edge.421" "edge.346" "edge.347" \ "edge.176" "edge.349" volume create wireframe "edge.156" "edge.155" "edge.153" "edge.154" \ "edge.418" "edge.419" "edge.420" "edge.421" "edge.348" "edge.337" \ "edge.349" "edge.166" volume create wireframe "edge.160" "edge.163" "edge.164" "edge.154" \ "edge.416" "edge.417" "edge.420" "edge.421" "edge.142" "edge.104" \ "edge.176" "edge.166" / 7 edge create straight "vertex.119" "vertex.219" edge create straight "vertex.118" "vertex.224" edge create straight "vertex.120" "vertex.220" edge create straight "vertex.117" "vertex.225"
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Appendix F (Continued) 263edge create straight "vertex.116" "vertex.221" edge create straight "vertex.113" "vertex.226" edge create straight "vertex.115" "vertex.74" edge create straight "vertex.114" "vertex.122" volume create wireframe "edge.182" "edge.183" "edge.181" "edge.184" \ "edge.422" "edge.423" "edge.424" "edge.425" "edge.350" "edge.339" \ "edge.351" "edge.352" volume create wireframe "edge.183" "edge.185" "edge.187" "edge.179" \ "edge.422" "edge.424" "edge.426" "edge.428" "edge.339" "edge.341" \ "edge.128" "edge.343" volume create wireframe "edge.181" "edge.186" "edge.188" "edge.177" \ "edge.423" "edge.425" "edge.427" "edge.429" "edge.351" "edge.353" \ "edge.200" "edge.355" volume create wireframe "edge.180" "edge.179" "edge.177" "edge.178" \ "edge.426" "edge.427" "edge.428" "edge.429" "edge.354" "edge.343" \ "edge.355" "edge.190" volume create wireframe "edge.184" "edge.187" "edge.188" "edge.178" \ "edge.424" "edge.425" "edge.428" "edge.429" "edge.352" "edge.128" \ "edge.200" "edge.190" / 8 edge create straight "vertex.135" "vertex.221" edge create straight "vertex.134" "vertex.226" edge create straight "vertex.136" "vertex.74" edge create straight "vertex.133" "vertex.122" edge create straight "vertex.132" "vertex.222" edge create straight "vertex.129" "vertex.227" edge create straight "vertex.131" "vertex.90" edge create straight "vertex.130" "vertex.138" volume create wireframe "edge.206" "edge.207" "edge.205" "edge.208" \ "edge.430" "edge.431" "edge.432" "edge.433" "edge.354" "edge.343" \ "edge.355" "edge.190" volume create wireframe "edge.207" "edge.209" "edge.211" "edge.203" \ "edge.430" "edge.432" "edge.434" "edge.436" "edge.343" "edge.344" \ "edge.152" "edge.346" volume create wireframe "edge.205" "edge.210" "edge.212" "edge.201" \ "edge.431" "edge.433" "edge.435" "edge.437" "edge.355" "edge.356" \ "edge.224" "edge.358" volume create wireframe "edge.204" "edge.203" "edge.201" "edge.202" \ "edge.434" "edge.435" "edge.436" "edge.437" "edge.357" "edge.346" \ "edge.358" "edge.214" volume create wireframe "edge.208" "edge.211" "edge.212" "edge.202" \ "edge.432" "edge.433" "edge.436" "edge.437" "edge.190" "edge.152" \ "edge.224" "edge.214" / 9 edge create straight "vertex.151" "vertex.222" edge create straight "vertex.150" "vertex.227" edge create straight "vertex.152" "vertex.90" edge create straight "vertex.149" "vertex.138" edge create straight "vertex.148" "vertex.223" edge create straight "vertex.145" "vertex.228" edge create straight "vertex.147" "vertex.106" edge create straight "vertex.146" "vertex.154" volume create wireframe "edge.230" "edge.231" "edge.229" "edge.232" \
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Appendix F (Continued) 264 "edge.438" "edge.439" "edge.440" "edge.441" "edge.357" "edge.346" \ "edge.358" "edge.214" volume create wireframe "edge.231" "edge.233" "edge.235" "edge.227" \ "edge.438" "edge.440" "edge.442" "edge.444" "edge.346" "edge.347" \ "edge.176" "edge.349" volume create wireframe "edge.229" "edge.234" "edge.236" "edge.225" \ "edge.439" "edge.441" "edge.443" "edge.445" "edge.358" "edge.359" \ "edge.248" "edge.361" volume create wireframe "edge.228" "edge.227" "edge.225" "edge.226" \ "edge.442" "edge.443" "edge.444" "edge.445" "edge.360" "edge.349" \ "edge.361" "edge.238" volume create wireframe "edge.232" "edge.235" "edge.236" "edge.226" \ "edge.440" "edge.441" "edge.444" "edge.445" "edge.214" "edge.176" \ "edge.248" "edge.238" / 10 edge create straight "vertex.167" "vertex.224" edge create straight "vertex.166" "vertex.229" edge create straight "vertex.168" "vertex.225" edge create straight "vertex.165" "vertex.230" edge create straight "vertex.164" "vertex.226" edge create straight "vertex.161" "vertex.231" edge create straight "vertex.163" "vertex.122" edge create straight "vertex.162" "vertex.170" volume create wireframe "edge.254" "edge.255" "edge.253" "edge.256" \ "edge.446" "edge.447" "edge.448" "edge.449" "edge.362" "edge.351" \ "edge.363" "edge.364" volume create wireframe "edge.255" "edge.257" "edge.259" "edge.251" \ "edge.446" "edge.448" "edge.450" "edge.452" "edge.351" "edge.353" \ "edge.200" "edge.355" volume create wireframe "edge.253" "edge.258" "edge.260" "edge.249" \ "edge.447" "edge.449" "edge.451" "edge.453" "edge.363" "edge.365" \ "edge.272" "edge.367" volume create wireframe "edge.252" "edge.251" "edge.249" "edge.250" \ "edge.450" "edge.451" "edge.452" "edge.453" "edge.366" "edge.355" \ "edge.367" "edge.262" volume create wireframe "edge.256" "edge.259" "edge.260" "edge.250" \ "edge.448" "edge.449" "edge.452" "edge.453" "edge.364" "edge.200" \ "edge.272" "edge.262" / 11 edge create straight "vertex.183" "vertex.226" edge create straight "vertex.182" "vertex.231" edge create straight "vertex.184" "vertex.122" edge create straight "vertex.181" "vertex.170" edge create straight "vertex.180" "vertex.227" edge create straight "vertex.177" "vertex.232" edge create straight "vertex.179" "vertex.138" edge create straight "vertex.178" "vertex.186" volume create wireframe "edge.278" "edge.279" "edge.277" "edge.280" \ "edge.454" "edge.455" "edge.456" "edge.457" "edge.366" "edge.355" \ "edge.367" "edge.262" volume create wireframe "edge.279" "edge.281" "edge.283" "edge.275" \ "edge.454" "edge.456" "edge.458" "edge.460" "edge.355" "edge.356" \ "edge.224" "edge.358"
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Appendix F (Continued) 265volume create wireframe "edge.277" "edge.282" "edge.284" "edge.273" \ "edge.455" "edge.457" "edge.459" "edge.461" "edge.367" "edge.368" \ "edge.296" "edge.370" volume create wireframe "edge.276" "edge.275" "edge.273" "edge.274" \ "edge.458" "edge.459" "edge.460" "edge.461" "edge.369" "edge.358" \ "edge.370" "edge.286" volume create wireframe "edge.280" "edge.283" "edge.284" "edge.274" \ "edge.456" "edge.457" "edge.460" "edge.461" "edge.262" "edge.224" \ "edge.296" "edge.286" / 12 edge create straight "vertex.199" "vertex.227" edge create straight "vertex.198" "vertex.232" edge create straight "vertex.200" "vertex.138" edge create straight "vertex.197" "vertex.186" edge create straight "vertex.196" "vertex.228" edge create straight "vertex.193" "vertex.233" edge create straight "vertex.195" "vertex.154" edge create straight "vertex.194" "vertex.202" volume create wireframe "edge.302" "edge.303" "edge.301" "edge.304" \ "edge.462" "edge.463" "edge.464" "edge.465" "edge.369" "edge.358" \ "edge.370" "edge.286" volume create wireframe "edge.303" "edge.305" "edge.307" "edge.299" \ "edge.462" "edge.464" "edge.466" "edge.468" "edge.358" "edge.359" \ "edge.248" "edge.361" volume create wireframe "edge.301" "edge.306" "edge.308" "edge.297" \ "edge.463" "edge.465" "edge.467" "edge.469" "edge.370" "edge.371" \ "edge.320" "edge.373" volume create wireframe "edge.300" "edge.299" "edge.297" "edge.298" \ "edge.466" "edge.467" "edge.468" "edge.469" "edge.372" "edge.361" \ "edge.373" "edge.310" volume create wireframe "edge.304" "edge.307" "edge.308" "edge.298" \ "edge.464" "edge.465" "edge.468" "edge.469" "edge.286" "edge.248" \ "edge.320" "edge.310" / / EVAPORATOR / coordinate create cartesian oldsystem "c_sys.1" offset $W 0 $H axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation face create width 0.6 height 0.4 offset 0.2 0 0 zxplane rectangle face create width 0.4 height 0.4 offset 0.2 0 0 zxplane rectangle face create width 0.7 height 0.5 offset 0.2 0 0 zxplane rectangle face create width 0.5 height 0.9 offset 0.2 0 0 zxplane rectangle face create width 0.3 height 0.7 offset 0.2 0 0 zxplane rectangle / face create width 4 height 8 offset 0.25 0 0 yzplane rectangle volume split "volume.2" faces "face.355" connected / face split "face.352" connected face "face.350" face subtract "face.352" faces "face.353" keeptool face split "face.353" connected face "face.351" face subtract "face.353" faces "face.350" face split "face.353" connected keeptool face "face.354"
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Appendix F (Continued) 266face split "face.364" connected face "face.354" face delete "face.351" lowertopology / volume create translate "face.362" "face.352" "face.353" "face.364" \ "face.365" "face.354" vector 0 2 0 volume split "volume.2" volumes "volume.104" connected bientity volume split "volume.2" volumes "volume.105" connected bientity volume split "volume.2" volumes "volume.106" connected bientity volume split "volume.2" volumes "volume.107" connected bientity volume split "volume.114" volumes "volume.108" connected bientity volume split "volume.114" volumes "volume.109" connected bientity volume delete "volume.114" lowertopology volume delete "volume.8" "volume.10" "volume.12" "volume.14" "volume.16" \ "volume.18" "volume.20" "volume.22" "volume.24" "volume.26" "volume.28" \ "volume.30" lowertopology / / / MESHING / default set "MESH.NODES.EDGE" numeric 2 default set "MESH.NODES.HEX" numeric 8 / / MESH UNOCCUPIED SPACE / volume mesh "volume.2" "volume.103" submap size $S / / MESH FLOOR, WALLS, CEILING / edge mesh "edge.25" "edge.26" "edge.27" "edge.28" "edge.29" "edge.30" \ "edge.31" "edge.32" successive ratio1 $R intervals $N volume mesh "volume.3" "volume.4" "volume.5" "volume.6" map / / MESH PACKAGE ENVELOPES / edge mesh "edge.374" "edge.375" "edge.376" "edge.377" "edge.378" "edge.379" \ "edge.380" "edge.381" "edge.382" "edge.383" "edge.384" "edge.385" \ "edge.386" "edge.387" "edge.388" "edge.389" "edge.390" "edge.391" \ "edge.392" "edge.393" "edge.394" "edge.395" "edge.396" "edge.397" \ "edge.398" "edge.399" "edge.400" "edge.401" "edge.402" "edge.403" \ "edge.404" "edge.405" "edge.406" "edge.407" "edge.408" "edge.409" \ "edge.410" "edge.411" "edge.412" "edge.413" "edge.414" "edge.415" \ "edge.416" "edge.417" "edge.418" "edge.419" "edge.420" "edge.421" \ "edge.422" "edge.423" "edge.424" "edge.425" "edge.426" "edge.427" \ "edge.428" "edge.429" "edge.430" "edge.431" "edge.432" "edge.433" \ "edge.434" "edge.435" "edge.436" "edge.437" "edge.438" "edge.439" \ "edge.440" "edge.441" "edge.442" "edge.443" "edge.444" "edge.445" \ "edge.446" "edge.447" "edge.448" "edge.449" "edge.450" "edge.451" \ "edge.452" "edge.453" "edge.454" "edge.455" "edge.456" "edge.457" \ "edge.458" "edge.459" "edge.460" "edge.461" "edge.462" "edge.463" \
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Appendix F (Continued) 267 "edge.464" "edge.465" "edge.466" "edge.467" "edge.468" "edge.469" \ successive ratio1 $R intervals $N / volume mesh "volume.43" "volume.44" "volume.45" "volume.46" "volume.47" \ "volume.48" "volume.49" "volume.50" "volume.51" "volume.52" "volume.53" \ "volume.54" "volume.55" "volume.56" "volume.57" "volume.58" "volume.59" \ "volume.60" "volume.61" "volume.62" "volume.63" "volume.64" "volume.65" \ "volume.66" "volume.67" "volume.68" "volume.69" "volume.70" "volume.71" \ "volume.72" "volume.73" "volume.74" "volume.75" "volume.76" "volume.77" \ "volume.78" "volume.79" "volume.80" "volume.81" "volume.82" "volume.83" \ "volume.84" "volume.85" "volume.86" "volume.87" "volume.88" "volume.89" \ "volume.90" "volume.91" "volume.92" "volume.93" "volume.94" "volume.95" \ "volume.96" "volume.97" "volume.98" "volume.99" "volume.100" "volume.101" \ "volume.102" map size $S / / MESH PACKAGES / volume mesh "volume.7" "volume.9" "volume.11" "volume.13" "volume.15" \ "volume.17" "volume.19" "volume.21" "volume.23" "volume.25" "volume.27" \ "volume.29" map / / MESH EVAPORATOR INLET/OUTLET / edge mesh "edge.544" "edge.541" "edge.548" "edge.545" successive ratio1 1 \ intervals $M blayer create first $F growth $R rows ($N1) transition 1 trows 0 blayer attach "b_layer.1" face "face.416" "face.416" "face.416" "face.418" \ "face.418" "face.418" "face.417" "face.417" "face.417" "face.419" \ "face.419" "face.419" edge "edge.635" "edge.640" "edge.636" "edge.655" \ "edge.650" "edge.656" "edge.638" "edge.643" "edge.637" "edge.658" \ "edge.653" "edge.657" blayer create first $F growth $R rows ($N1) transition 1 trows 0 blayer attach "b_layer.2" face "face.357" "face.420" "face.357" "face.420" \ "face.427" "face.421" "face.427" "face.421" edge "edge.673" "edge.689" \ "edge.665" "edge.681" "edge.690" "edge.674" "edge.682" "edge.666" /
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Appendix F (Continued) 268face modify "face.416" side "vertex.350" face modify "face.416" side "vertex.351" face modify "face.416" side "vertex.354" face modify "face.416" side "vertex.355" face modify "face.418" side "vertex.362" face modify "face.418" side "vertex.363" face modify "face.418" side "vertex.358" face modify "face.418" side "vertex.359" face modify "face.357" side "vertex.300" face modify "face.357" side "vertex.298" face modify "face.357" side "vertex.380" face modify "face.357" side "vertex.374" face modify "face.420" side "vertex.305" face modify "face.420" side "vertex.303" face modify "face.420" side "vertex.388" face modify "face.420" side "vertex.382" face mesh "face.416" "face.418" "face.357" "face.420" map volume mesh "volume.104" cooper source "face.417" "face.416" volume mesh "volume.105" cooper source "face.419" "face.418" volume mesh "volume.106" cooper source "face.357" "face.421" volume mesh "volume.107" cooper source "face.420" "face.427" volume mesh "volume.108" "volume.109" map / / PHYSICAL SETTINGS / solver select "FIDAP" / / SUBDOMAIN SETTINGS / physics create "products" ctype "SOLID" volume "volume.7" "volume.9" \ "volume.11" "volume.13" "volume.15" "volume.17" "volume.19" "volume.21" \ "volume.23" "volume.25" "volume.27" "volume.29" physics create "air" ctype "FLUID" volume "volume.3" "volume.4" "volume.5" \ "volume.6" "volume.104" "volume.43" "volume.44" "volume.45" "volume.46" \ "volume.47" "volume.48" "volume.49" "volume.50" "volume.51" "volume.52" \ "volume.53" "volume.54" "volume.55" "volume.56" "volume.57" "volume.58" \ "volume.59" "volume.60" "volume.61" "volume.62" "volume.63" "volume.64" \ "volume.65" "volume.66" "volume.67" "volume.68" "volume.69" "volume.70" \ "volume.71" "volume.72" "volume.73" "volume.74" "volume.75" "volume.76" \ "volume.77" "volume.78" "volume.79" "volume.80" "volume.81" "volume.82" \ "volume.83" "volume.84" "volume.85" "volume.86" "volume.87" "volume.88" \
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Appendix F (Continued) 269 "volume.89" "volume.90" "volume.91" "volume.92" "volume.93" "volume.94" \ "volume.95" "volume.96" "volume.97" "volume.98" "volume.99" "volume.100" \ "volume.101" "volume.102" "volume.103" "volume.105" "volume.106" \ "volume.108" "volume.107" "volume.2" "volume.109" / / BOUNDARY SETTINGS / physics create "floor" btype "WALL" face "face.1" physics create "ceiling" btype "WALL" face "face.6" physics create "walls" btype "WALL" face "face.3" "face.4" / physics create "containers" btype "WALL" face "face.25" "face.27" "face.28" \ "face.30" "face.29" "face.38" "face.40" "face.42" "face.37" "face.41" \ "face.50" "face.52" "face.54" "face.49" "face.53" "face.62" "face.64" \ "face.66" "face.61" "face.65" "face.74" "face.76" "face.78" "face.73" \ "face.77" "face.86" "face.88" "face.90" "face.85" "face.89" "face.98" \ "face.100" "face.102" "face.97" "face.101" "face.110" "face.112" "face.114" \ "face.109" "face.113" "face.122" "face.124" "face.126" "face.121" \ "face.125" "face.134" "face.136" "face.138" "face.133" "face.137" \ "face.146" "face.148" "face.150" "face.145" "face.149" "face.158" \ "face.160" "face.162" "face.157" "face.161" / physics create "evap_cover" btype "WALL" face "face.395" "face.370" \ "face.373" "face.371" "face.406" "face.387" "face.382" "face.379" \ "face.383" "face.398" physics create "evap_blow" btype "PLOT" face "face.399" "face.413" "face.405" physics create "evap_suct" btype "PLOT" face "face.388" "face.410" "face.394" / physics create "symmetry" btype "PLOT" face "face.358" "face.425" "face.16" \ "face.24" "face.21" "face.18" "face.417" "face.419" "face.421" "face.427" \ "face.11" "face.431" "face.204" "face.424" "face.13" "face.23" "face.17" \ "face.20" "face.416" "face.418" "face.357" "face.420" "face.430" "face.426" \ "face.206" "face.210" "face.213" "face.216" "face.218" "face.222" \ "face.225" "face.228" "face.234" "face.237" "face.240" "face.242" \ "face.246" "face.249" "face.252" "face.254" "face.258" "face.261" \ "face.264" "face.266" "face.270" "face.273" "face.276" "face.278" \ "face.282" "face.285" "face.288" "face.290" "face.294" "face.297" \ "face.300" "face.302" "face.306" "face.309" "face.312" "face.314" \ "face.318" "face.321" "face.324" "face.326" "face.330" "face.333" \
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Appendix F (Continued) 270 "face.336" "face.338" "face.342" "face.345" "face.348" "face.230" \ "face.26" "face.39" "face.51" "face.63" "face.75" "face.87" "face.99" \ "face.111" "face.123" "face.135" "face.147" "face.159" / / EXPORT MESH / $ID = GETIDENT() $NEUTRALFILE = $ID + ".FDNEUT" export fidap $NEUTRALFILE F.4 Simulation Settings for 3D Model: FIDAP Commands / FIDAP Input File / SIMULATION SETTINGS / PROJECT: Refrigerated Warehouse with Ceiling Type Cooling Units / Threedimensional (3D) model, SI units / / / Neutral file name $NEUTRALFILE = "mesh.FDNEUT" / / CONVERSION OF NEUTRAL FILE TO FIDAP Database / FICONV( NEUTRAL ) INPUT( FILE=$NEUTRALFILE ) OUTPUT( DELETE ) END / TITLE Refrigerated Warehouse, 3D model / / CONSTANTS / $V_SUPPLY = 0.5 $T_SUPPLY = 0 $F_LIGHT = 10 / IF ( $T_SUPPLY .EQ. 0 ) $T_MIN = 1.E20 ELSE $T_MIN = $T_SUPPLY ENDIF / $G = 9.8 $RHO = 1.293 $MU = 17.20E6 $K = 24.07E3 $CP = 1004. $BETA = 3.663E3 $TREF = 0
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Appendix F (Continued) 271/ $RHO_2 = 840 $K_2 = 0.52 $CP_2 = 3.79E3 / $H_CCF = 1.18 $T_GROUND = 15 $H_PUR = 0.23 $T_AMBIENT = 35 $T_CEILING = $T_AMBIENT + $F_LIGHT/$H_PUR / / ABBREVIATIONS / CCF: concrete floor / PUR: polyurethane / FIPREP / / PROBLEM SETUP / GRAVITY( MAGNITUDE = $G ) PROBLEM( 3D, TURBULENT, NONLINEAR, BUOYANCY ) EXECUTION( NEWJOB ) PRINTOUT( NONE ) DATAPRINT( NONE ) / / CONTINUUM ENTITIES / ENTITY( NAME = "air", FLUID, PROPERTY = "air" ) ENTITY( NAME = "products", SOLID, PROPERTY = "products" ) / / BOUNDARY ENTITIES / ENTITY( NAME = "symmetry", PLOT ) ENTITY( NAME = "floor", CONVECTION, MCNV = "floor" ) ENTITY( NAME = "ceiling", CONVECTION, MCNV = "ceiling" ) ENTITY( NAME = "walls", CONVECTION, MCNV = "walls" ) ENTITY( NAME = "containers", WALL, ATTACH = "air", NATTACH = "products" ) ENTITY( NAME = "evap_cover", WALL ) ENTITY( NAME = "evap_blow", PLOT ) ENTITY( NAME = "evap_suct", PLOT ) / / SOLUTION PARAMETERS / PRESSURE( MIXED = 1.E8, DISCONTINUOUS ) SOLUTION( SEGREGATED = 100, CR, CGS, VELCONV = .01, NCGC = 1.E6, SCGC = 1.E6, SCHANGE = .0 ) RELAX( HYBRID ) OPTIONS( UPWINDING ) POSTPROCESS( RESIDUAL ) CLIPPING( MINIMUM ) 0 0 0 0 $T_MIN /
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Appendix F (Continued) 272/ MATERIAL PROPERTIES / / Partial list of Material Properties data / DENSITY( SET = "air", CONSTANT = $RHO ) VISCOSITY( SET = "air", CONSTANT = $MU, MIXLENGTH ) CONDUCTIVITY( SET = "air", CONSTANT = $K ) SPECIFICHEAT( SET = "air", CONSTANT = $CP ) VOLUMEXPANSION( SET = "air", CONSTANT = $BETA, REFTEMP = $TREF ) / DENSITY( SET = "products", CONSTANT = $RHO_2 ) CONDUCTIVITY( SET = "products", CONSTANT = $K_2 ) SPECIFICHEAT( SET = "products", CONSTANT = $CP_2 ) / HTRANSFER( SET = "floor" CONSTANT = $H_CCF, REFTEMP = $T_GROUND ) HTRANSFER( SET = "ceiling" CONSTANT = $H_PUR, REFTEMP = $T_CEILING) HTRANSFER( SET = "walls" CONSTANT = $H_PUR, REFTEMP = $T_AMBIENT ) / / INITIAL AND BOUNDARY CONDITIONS / BCNODE( VELO, ZERO, ENTITY = "evap_cover" ) BCNODE( VELO, ZERO, ENTITY = "floor" ) BCNODE( VELO, ZERO, ENTITY = "ceiling" ) BCNODE( VELO, ZERO, ENTITY = "walls" ) BCNODE( VELO, ZERO, ENTITY = "containers" ) BCNODE( UY, ZERO, ENTITY = "symmetry" ) BCNODE( VELO, CONSTANT, X = $V_SUPPLY, Y = 0, Z = 0, ENTITY = "evap_blow" ) / BCNODE( TEMP, CONSTANT = $T_SUPPLY, ENTITY = "evap_blow" ) / END / CREATE( FISOLV ) RUN( FISOLV, BACKGROUND )
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273 Appendix G: FIDAP Preprocessing Input for Chapter 8 G.1 Geometry and Meshing: FIDAP Commands / FIDAP Input File / GEOMETRY and MESHING / PROJECT: AirConditioned Room with Ceiling Fan / Twodimensional (2D) model, SI units / NOTE: The parameters $L1 to $L19 are NOT the same as the dimensions / L1 to L12 presented in the text. TITLE Airconditioned room with ceiling fan, 2D model // FIGEN FIGEN( ELEM = 1, POIN = 1, CURV = 1, SURF = 1, NODE = 0, MEDG = 1, MLOO = 1, MFAC = 1, BEDG = 1, SPAV = 1, MSHE = 1, MSOL = 1, COOR = 1 ) / Width of room $L1 = 3.70 / Distance of fan center from left wall $L2 = 1.85 / Width of fan site $L3 = 1.70 / Distance of body center from fan center $L4 = 0 / Width of body $L5 = 0.26 / Thickness of air zone around body $L6 = 0.10 / Diameter of motorlights neck $L7 = 0.10 / Span from neck of motorlights $L8 = 0.10 / Thickness of air zone around motorlights $L9 = 0.05 / Width of fan blade span, L10 < L3 $L10 = 1.07 / Height of room $L11 = 2.70 / Height of inlet (bottom edge) from floor $L12 = 2.33 / Size of inlet $L13 = 0.20 / Height of outlet (bottom edge) from floor $L14 = 0.20 / Size of outlet $L15 = 0.25 / Gap from floor to body $L16 = 0.20
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Appendix G (Continued) 274/ Height of body $L17 = 1.70 / Height of fan plane $L18 = 2.30 / Size of smoke source $L19 = 0.05 // COORDINATES $NX = 18 DECLARE $XP[1:$NX] $XP[1] = 0 $XP[2] = $XP[1]+$L1 $XP[3] = $XP[1]+$L2 $XP[4] = $XP[3]$L3/2 $XP[5] = $XP[3]+$L3/2 $XP[6] = $XP[3]+$L4 $XP[7] = $XP[6]$L5/2 $XP[8] = $XP[6]+$L5/2 $XP[9] = $XP[7]$L6 $XP[10] = $XP[8]+$L6 $XP[11] = $XP[3]$L7/2 $XP[12] = $XP[3]+$L7/2 $XP[13] = $XP[11]$L8 $XP[14] = $XP[12]+$L8 $XP[15] = $XP[13]$L9 $XP[16] = $XP[14]+$L9 $XP[17] = $XP[3]$L10/2 $XP[18] = $XP[3]+$L10/2 $NY = 19 DECLARE $YP[1:$NY] $YP[1] = 0 $YP[2] = $YP[1]+$L11 $YP[3] = $YP[1]+$L12 $YP[4] = $YP[3]+$L13 $YP[5] = $YP[1]+$L14 $YP[6] = $YP[5]+$L15 $YP[7] = $YP[1]+$L16 $YP[8] = $YP[1]+$L17 $YP[9] = $YP[1]+$L18 $YP[10] = $YP[9]+$L9 $YP[11] = $YP[10]+0.10 $YP[12] = $YP[11]+$L9 $YP[13] = $YP[9]$L9 $YP[14] = $YP[13]0.10 $YP[15] = $YP[14]0.10 $YP[16] = $YP[15]$L9 $YP[17] = $YP[8]+$L6 $YP[18] = $YP[8]$L5/2 $YP[19] = $YP[18]$L19 // Lengths $NL = 71
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Appendix G (Continued) 275DECLARE $L[1:$NL] $L[1] = $YP[3]$YP[1] $L[2] = $YP[4]$YP[3] $L[3] = $YP[2]$YP[4] $L[4] = $XP[4]$XP[1] $L[5] = $XP[5]$XP[4] $L[6] = $XP[2]$XP[5] $L[7] = $YP[2]$YP[6] $L[8] = $YP[6]$YP[5] $L[9] = $YP[5]$YP[1] $L[10] = $L[6] $L[11] = $L[5] $L[12] = $L[4] $L[13] = $YP[7]$YP[1] $L[14] = $YP[17]$YP[7] $L[15] = $YP[16]$YP[17] $L[16] = $YP[9]$YP[16] $L[17] = $YP[12]$YP[9] $L[18] = $YP[2]$YP[12] $L[19] = $L[13] $L[20] = $L[14] $L[21] = $L[15] $L[22] = $L[16] $L[23] = $L[17] $L[24] = $L[18] $L[25] = $XP[9]$XP[4] $L[26] = $XP[7]$XP[9] $L[27] = $XP[8]$XP[7] $L[28] = $XP[10]$XP[8] $L[29] = $XP[5]$XP[10] $L[30] = $L[25] $L[31] = $XP[10]$XP[9] $L[32] = $L[29] $L[33] = $XP[15]$XP[4] $L[34] = $XP[16]$XP[15] $L[35] = $XP[5]$XP[16] $L[36] = $L[33] $L[37] = $L[34] $L[38] = $L[35] $L[39] = $YP[19]$YP[7] $L[40] = $YP[18]$YP[19] $L[41] = ($XP[8]$XP[7])*PI/2
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Appendix G (Continued) 276$L[42] = $L[40] $L[43] = $L[39] $L[44] = $L[14] $L[45] = $L[20] $L[46] = ($YP[15]$YP[13])*PI/2 $L[47] = $XP[12]$XP[11] $L[48] = $L[46] $L[49] = $YP[9]$YP[13] $L[50] = $YP[10]$YP[9] $L[51] = $XP[14]$XP[12] $L[52] = $YP[11]$YP[10] $L[53] = $XP[14]$XP[13] $L[54] = $L[52] $L[55] = $L[51] $L[56] = $L[50] $L[57] = $L[49] $L[58] = $L[16] $L[59] = $L[17] $L[60] = $L[22] $L[61] = $L[23] $L[62] = $XP[3]$YP[15] $L[63] = $XP[15]$XP[17] $L[64] = $XP[17]$XP[4] $L[65] = $L[62] $L[66] = $L[63] $L[67] = $L[64] $L[68] = $YP[18]$YP[7] $L[69] = $YP[17]$YP[18] $L[70] = $L[68] $L[71] = $L[69] // Mesh Intervals and Grading Factors DECLARE $M[1:$NL] DECLARE $R1[1:$NL] DECLARE $R2[1:$NL] $Lm = 0.025 $Lb = 0.005 DO( $I = 1, $I .LE. $NL ) $M[$I] = 2*INT($L[$I]/2/$Lm+0.5) IF($M[$I] .LT. 16 ) $M[$I] = 16 ENDIF ENDDO $M[46] = 4*$M[62] $M[58] = $M[46]/2 $M[48] = 4*$M[65]
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Appendix G (Continued) 277$M[60] = $M[48]/2 $M[34] = $M[47]+$M[46]/4+$M[48]/4 $M[51] = $M[65] $M[52] = $M[61] $M[53] = $M[37] $M[54] = $M[59] $M[55] = $M[62] $M[16] = $M[58] $M[33] = $M[63]+$M[64] $M[22] = $M[60] $M[35] = $M[66]+$M[67] $M[17] = $M[59] $M[36] = $M[63]+$M[64] $M[23] = $M[61] $M[38] = $M[66]+$M[67] $M[5] = $M[36]+$M[37]+$M[38] $M[31] = $M[33]+$M[34]+$M[35]$M[30]$M[32] $M[41] = 2*$M[31] $M[69] = $M[41]/4 $M[71] = $M[41]/4 $M[68] = $M[39]+$M[40] $M[70] = $M[42]+$M[43] $M[14] = $M[68]+$M[69] $M[20] = $M[70]+$M[71] $M[25] = $M[30] $M[29] = $M[32] $M[11] = $M[25]+$M[26]+$M[27]+$M[28]+$M[29] $M[1] = $M[13]+$M[14]+$M[15]+$M[16]+$M[17]+$M[18]$M[2]$M[3] $M[7] = $M[19]+$M[20]+$M[21]+$M[22]+$M[23]+$M[24]$M[8]$M[9] // ADD POINTS POINT( ADD, COOR ) $XP[1] $YP[1] $XP[1] $YP[3] $XP[1] $YP[4] $XP[1] $YP[2] $XP[4] $YP[2] $XP[5] $YP[2] $XP[2] $YP[2] $XP[2] $YP[6] $XP[2] $YP[5] $XP[2] $YP[1] $XP[5] $YP[1] $XP[4] $YP[1]
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Appendix G (Continued) 278$XP[4] $YP[7] $XP[4] $YP[17] $XP[4] $YP[16] $XP[4] $YP[9] $XP[4] $YP[12] $XP[5] $YP[7] $XP[5] $YP[17] $XP[5] $YP[16] $XP[5] $YP[9] $XP[5] $YP[12] $XP[9] $YP[7] $XP[7] $YP[7] $XP[8] $YP[7] $XP[10] $YP[7] $XP[9] $YP[17] $XP[10] $YP[17] $XP[15] $YP[16] $XP[16] $YP[16] $XP[15] $YP[12] $XP[16] $YP[12] $XP[7] $YP[19] $XP[7] $YP[18] $XP[6] $YP[8] $XP[8] $YP[18] $XP[8] $YP[19] $XP[11] $YP[13] $XP[13] $YP[14] $XP[11] $YP[15] $XP[12] $YP[15] $XP[14] $YP[14] $XP[12] $YP[13] $XP[12] $YP[9] $XP[12] $YP[10] $XP[14] $YP[10] $XP[14] $YP[11] $XP[13] $YP[11] $XP[13] $YP[10] $XP[11] $YP[10] $XP[11] $YP[9] $XP[15] $YP[9] $XP[17] $YP[9] $XP[16] $YP[9] $XP[18] $YP[9] $XP[9] $YP[18]
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Appendix G (Continued) 279$XP[10] $YP[18] // ADD LINES POINT( SELE, ID) 1 12 1 CURVE( ADD, LINE ) POINT( SELE, ID) 12 17 5 CURVE( ADD, LINE ) POINT( SELE, ID) 11 18 22 6 CURVE( ADD, LINE ) POINT( SELE, ID) 13 23 26 18 CURVE( ADD, LINE ) POINT( SELE, ID) 14 27 28 19 CURVE( ADD, LINE ) POINT( SELE, ID) 15 29 30 20 CURVE( ADD, LINE ) POINT( SELE, ID) 17 31 32 22 CURVE( ADD, LINE ) POINT( SELE, ID) 24 33 34 CURVE( ADD, LINE ) POINT( SELE, ID) 34 36 CURVE( ADD, ARC, 3POINTS )
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Appendix G (Continued) 280 POINT( SELE, ID) 36 37 25 CURVE( ADD, LINE ) POINT( SELE, ID) 23 27 CURVE( ADD, LINE ) POINT( SELE, ID) 26 28 CURVE( ADD, LINE ) POINT( SELE, ID) 38 40 CURVE( ADD, ARC, 3POINTS ) POINT( SELE, ID) 40 41 CURVE( ADD, LINE ) POINT( SELE, ID) 41 43 CURVE( ADD, ARC, 3POINTS ) POINT( SELE, ID) 43 51 38 CURVE( ADD, LINE ) POINT( SELE, ID) 29 52 31 CURVE( ADD, LINE ) POINT( SELE, ID) 30 54 32 CURVE( ADD, LINE ) POINT( SELE, ID) 51 53 16 CURVE( ADD, LINE ) POINT( SELE, ID) 44 54 55
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Appendix G (Continued) 28121 CURVE( ADD, LINE ) CURVE( SELE, ID = 44 ) POINT( SELE, ID = 56 ) CURVE( SPLIT, KEEP ) CURVE( SELE, ID = 45 ) POINT( SELE, ID = 57 ) CURVE( SPLIT, KEEP ) // ADD SURFACES POINT( SELE, ID ) 4 7 1 10 SURFACE( ADD, POINT, ROWW = 2, NOADCURVES, INVISIBLE ) // ADD MESH EDGES CURVE( SELE, ID = 1 ) MEDGE( ADD, FRTL, INTE = $M[1], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 2 ) MEDGE( ADD, FRTL, INTE = $M[2], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 3 ) MEDGE( ADD, FRTL, INTE = $M[3], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 4 ) MEDGE( ADD, FRTL, INTE = $M[4], RATI = $Lb, 2RAT = $Lm, PCEN = 0 ) CURVE( SELE, ID = 5 ) MEDGE( ADD, SUCC, INTE = $M[5], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 6 ) MEDGE( ADD, FRTL, INTE = $M[6], RATI = $Lm, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 7 ) MEDGE( ADD, FRTL, INTE = $M[7], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 8 ) MEDGE( ADD, FRTL, INTE = $M[8], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 9 ) MEDGE( ADD, FRTL, INTE = $M[9], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 10 ) MEDGE( ADD, FRTL, INTE = $M[10], RATI = $Lb, 2RAT = $Lm, PCEN = 0 ) CURVE( SELE, ID = 11 ) MEDGE( ADD, SUCC, INTE = $M[11], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 12 ) MEDGE( ADD, FRTL, INTE = $M[12], RATI = $Lm, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 13 ) MEDGE( ADD, FRTL, INTE = $M[13], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 14 ) MEDGE( ADD, SUCC, INTE = $M[14], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 15 ) MEDGE( ADD, SUCC, INTE = $M[15], RATI = 0, 2RAT = 0, PCEN = 0 )
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Appendix G (Continued) 282CURVE( SELE, ID = 16 ) MEDGE( ADD, SUCC, INTE = $M[16], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 17 ) MEDGE( ADD, SUCC, INTE = $M[17], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 18 ) MEDGE( ADD, FRTL, INTE = $M[18], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 19 ) MEDGE( ADD, FRTL, INTE = $M[19], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 20 ) MEDGE( ADD, SUCC, INTE = $M[20], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 21 ) MEDGE( ADD, SUCC, INTE = $M[21], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 22 ) MEDGE( ADD, SUCC, INTE = $M[22], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 23 ) MEDGE( ADD, SUCC, INTE = $M[23], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 24 ) MEDGE( ADD, FRTL, INTE = $M[24], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 25 ) MEDGE( ADD, SUCC, INTE = $M[25], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 26 ) MEDGE( ADD, FRST, INTE = $M[26], RATI = 3, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 27 ) MEDGE( ADD, SUCC, INTE = $M[27], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 28 ) MEDGE( ADD, LSTF, INTE = $M[28], RATI = 3, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 29 ) MEDGE( ADD, SUCC, INTE = $M[29], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 30 ) MEDGE( ADD, SUCC, INTE = $M[30], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 31 ) MEDGE( ADD, SUCC, INTE = $M[31], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 32 ) MEDGE( ADD, SUCC, INTE = $M[32], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 33 ) MEDGE( ADD, SUCC, INTE = $M[33], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 34 ) MEDGE( ADD, SUCC, INTE = $M[34], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 35 ) MEDGE( ADD, SUCC, INTE = $M[35], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 36 ) MEDGE( ADD, SUCC, INTE = $M[36], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 37 ) MEDGE( ADD, SUCC, INTE = $M[37], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 38 ) MEDGE( ADD, SUCC, INTE = $M[38], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 39 ) MEDGE( ADD, FRTL, INTE = $M[39], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 40 ) MEDGE( ADD, SUCC, INTE = $M[40], RATI = 0, 2RAT = 0, PCEN = 0 )
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Appendix G (Continued) 283CURVE( SELE, ID = 41 ) MEDGE( ADD, SUCC, INTE = $M[41], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 42 ) MEDGE( ADD, SUCC, INTE = $M[42], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 43 ) MEDGE( ADD, FRTL, INTE = $M[43], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 44 ) MEDGE( ADD, SUCC, INTE = $M[44], RATI = 0, 2RAT = 0, PCEN = 0, INVISIBLE ) CURVE( SELE, ID = 45 ) MEDGE( ADD, SUCC, INTE = $M[45], RATI = 0, 2RAT = 0, PCEN = 0, INVISIBLE ) CURVE( SELE, ID = 46 ) MEDGE( ADD, SUCC, INTE = $M[46], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 47 ) MEDGE( ADD, SUCC, INTE = $M[47], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 48 ) MEDGE( ADD, SUCC, INTE = $M[48], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 49 ) MEDGE( ADD, LSTF, INTE = $M[49], RATI = 2, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 50 ) MEDGE( ADD, FRST, INTE = $M[50], RATI = 2, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 51 ) MEDGE( ADD, SUCC, INTE = $M[51], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 52 ) MEDGE( ADD, SUCC, INTE = $M[52], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 53 ) MEDGE( ADD, SUCC, INTE = $M[53], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 54 ) MEDGE( ADD, SUCC, INTE = $M[54], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 55 ) MEDGE( ADD, SUCC, INTE = $M[55], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 56 ) MEDGE( ADD, LSTF, INTE = $M[56], RATI = 2, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 57 ) MEDGE( ADD, FRST, INTE = $M[57], RATI = 2, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 58 ) MEDGE( ADD, SUCC, INTE = $M[58], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 59 ) MEDGE( ADD, SUCC, INTE = $M[59], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 60 ) MEDGE( ADD, SUCC, INTE = $M[60], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 61 ) MEDGE( ADD, SUCC, INTE = $M[61], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 62 ) MEDGE( ADD, SUCC, INTE = $M[62], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 63 ) MEDGE( ADD, SUCC, INTE = $M[63], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 64 ) MEDGE( ADD, SUCC, INTE = $M[64], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 65 )
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Appendix G (Continued) 284MEDGE( ADD, SUCC, INTE = $M[65], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 66 ) MEDGE( ADD, SUCC, INTE = $M[66], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 67 ) MEDGE( ADD, SUCC, INTE = $M[67], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 68 ) MEDGE( ADD, FRTL, INTE = $M[68], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 69 ) MEDGE( ADD, SUCC, INTE = $M[69], RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 70 ) MEDGE( ADD, FRTL, INTE = $M[70], RATI = $Lb, 2RAT = $Lb, PCEN = 0 ) CURVE( SELE, ID = 71 ) MEDGE( ADD, SUCC, INTE = $M[71], RATI = 0, 2RAT = 0, PCEN = 0 ) MEDGE( SELE, ID ) 44 45 MEDGE( DELETE ) // ADD MESH LOOPS / Zone over fan plane around motor CURVE( SELE, ID ) 50 56 62 59 37 61 65 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 5, EDG3 = 1, EDG4 = 5 ) CURVE( SELE, ID ) 59 63 64 17 36 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, ID ) 61 66 67 23 38 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, ID ) 5 18 36 38 24 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 1, EDG3 = 3, EDG4 = 1 ) / Zone around body
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Appendix G (Continued) 285CURVE( SELE, ID ) 26 39 43 28 70 71 31 69 68 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 5, EDG3 = 1, EDG4 = 5 ) CURVE( SELE, ID ) 14 25 68 69 30 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, ID ) 20 29 70 71 32 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, ID ) 13 25 29 19 11 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 5, EDG3 = 1, EDG4 = 1 ) / Zone under fan plane around lights CURVE( SELE, ID ) 57 46 49 65 60 34 58 62 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 5 ) CURVE( SELE, ID ) 58 63 64 16 33 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, ID ) 60
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Appendix G (Continued) 28666 67 22 35 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, ID ) 15 33 35 21 32 31 30 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 3 ) / Inlet site CURVE( SELE, ID ) 12 13 18 4 3 2 1 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 6, EDG3 = 1, EDG4 = 3 ) / Outlet site CURVE( SELE, ID ) 6 10 19 24 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 6 ) // ADD MESH FACES $NLOOPS = LASTID( MLOOP_ID ) DO( $I = 1, $I .LE. $NLOOPS ) SURFACE( SELE, ID = 1 ) MLOOP( SELE, ID = $I) MFACE( ADD ) ENDDO // GENERATE MESH ELEMENT( SETD, QUAD, NODE = 9 ) ELEMENT( SETD, EDGE, NODE = 2 ) MFACE( SELE, ID ) 1 4 MFACE( MESH, MAP, ENTI = "air1" ) MFACE( SELE, ID ) 5
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Appendix G (Continued) 287MFACE( MESH, MAP, ENTI = "air2" ) MFACE( SELE, ID ) 6 $NLOOPS MFACE( MESH, MAP, ENTI = "air" ) // BOUNDARY MESH MEDGE( SELE, ID ) 2 MEDGE( MESH, MAP, ENTI = "inlet" ) MEDGE( SELE, ID ) 8 MEDGE( MESH, MAP, ENTI = "outlet" ) MEDGE( SELE, ID ) 27 39 41 43 MEDGE( MESH, MAP, ENTI = "body" ) MEDGE( SELE, ID ) 40 MEDGE( MESH, MAP, ENTI = "open1" ) MEDGE( SELE, ID ) 42 MEDGE( MESH, MAP, ENTI = "open2" ) MEDGE( SELE, ID ) 57 46 49 MEDGE( MESH, MAP, ENTI = "light" ) MEDGE( SELE, ID ) 50 56 MEDGE( MESH, MAP, ENTI = "motor" ) MEDGE( SELE, ID ) 62 63 MEDGE( MESH, MAP, ENTI = "blade1" ) MEDGE( SELE, ID ) 65 66 MEDGE( MESH, MAP, ENTI = "blade2" ) MEDGE( SELE, ID ) 1 3 7 9
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Appendix G (Continued) 288MEDGE( MESH, MAP, ENTI = "walls" ) MEDGE( SELE, ID ) 4 6 MEDGE( MESH, MAP, ENTI = "ceiling" ) MEDGE( SELE, ID ) 10 12 MEDGE( MESH, MAP, ENTI = "floor" ) END G.2 Simulation Settings: FIDAP Commands / FIDAP Input File / SIMULATION SETTINGS / PROJECT: AirConditioned Room with Ceiling Fan / Twodimensional (2D) model, SI units FIPREP / SI units / Reference temperature: 22 oC = 295 K $Tref = 22 $RHO = 1.1967 $MU = 18.273E6 $CP = 1.0043E3 $K = 25.776E3 $BETA = 3.3932E3 $NU = $MU/$RHO $G = 9.81 $SC_H2O = 0.60 DENSITY( SET = "air", CONS = $RHO ) VISCOSITY( SET = "air", CONS = $MU, MIXLENGTH ) SPECIFICHEAT( SET = "air", CONS = $CP ) CONDUCTIVITY( SET = "air", CONS = $K ) VOLUMEXPANSION( SET = "air", CONS = $BETA, REFTEMP = $Tref ) GRAVITY( MAGNITUDE = $G ) DIFFUSIVITY( SET = "H2O", CONS = $NU/$SC_H2O ) ENTITY( FLUI, NAME = "air",PROP = "air", SPEC = 1,MDIFF = "H2O" ) ENTITY( FLUI, NAME = "air1",PROP = "air", SPEC = 1,MDIFF = "H2O" ) ENTITY( FLUI, NAME = "air2",PROP = "air", SPEC = 1,MDIFF = "H2O" ) ENTITY( PLOT, NAME = "outlet" ) ENTITY( PLOT, NAME = "inlet" ) ENTITY( WALL, NAME = "walls" ) ENTITY( WALL, NAME = "ceiling" )
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Appendix G (Continued) 289ENTITY( WALL, NAME = "floor" ) ENTITY( WALL, NAME = "body" ) ENTITY( WALL, NAME = "open1" ) ENTITY( WALL, NAME = "open2" ) ENTITY( WALL, NAME = "light" ) ENTITY( WALL, NAME = "motor" ) ENTITY( PLOT, NAME = "blade1", ATTACH = "air1", NATTACH = "air" ) ENTITY( PLOT, NAME = "blade2", ATTACH = "air1", NATTACH = "air" ) $V_in = 1.0 $V_fan = 1.1 $T_in = $Tref $T_body = 34 $TF_lite = 300 $TF_motor = 10 $W_in = 0.0148 $WF_body = 5E7 BCNODE( VELO, ENTI = "inlet", CONS, X = $V_in, Y = 0 ) BCNODE( VELO, ENTI = "body", ZERO ) BCNODE( VELO, ENTI = "open1", ZERO ) BCNODE( VELO, ENTI = "open2", ZERO ) BCNODE( VELO, ENTI = "light", ZERO ) BCNODE( VELO, ENTI = "motor", ZERO ) BCNODE( VELO, ENTI = "walls", ZERO ) BCNODE( VELO, ENTI = "ceiling", ZERO ) BCNODE( VELO, ENTI = "floor", ZERO ) BCNODE( VELO, ENTI = "blade1", CONS, X = 0, Y = $V_fan ) BCNODE( VELO, ENTI = "blade2", CONS, X = 0, Y = $V_fan ) BCNODE( TEMP, ENTI = "inlet", CONS = $T_in ) BCNODE( TEMP, ENTI = "body", CONS = $T_body ) BCNODE( TEMP, ENTI = "open1", CONS = $T_body ) BCNODE( TEMP, ENTI = "open2", CONS = $T_body ) BCFLUX( HEAT, ENTI = "light", CONS = $TF_lite ) BCFLUX( HEAT, ENTI = "motor", CONS = $TF_motor ) BCNODE( SPEC = 1, ENTI = "inlet", CONS = $W_in ) BCFLUX( SPEC = 1, ENTI = "body", CONS = $WF_body ) BCFLUX( SPEC = 1, ENTI = "open1", CONS = $WF_body ) BCFLUX( SPEC = 1, ENTI = "open2", CONS = $WF_body ) CLIPPING( MINI ) 0, 0, 0, 0, $T_in, 0, 0, 0, $W_in CLIPPING( MAXI ) 0, 0, 0, 0, 0, 0, 0, 0, 1.0 DATAPRINT( NONE ) PRINTOUT( NONE ) OPTIONS( UPWI ) EXECUTION( NEWJ ) PRESSURE( PENA = 1E9, DISC )
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Appendix G (Continued) 290PROBLEM( 2D, NONLINEAR, TURBULENT, BUOYANCY, SPECIES = 1 ) SOLUTION( S.S. = 100, VELC = 0.0001, RESC = 0.0001, ACCF = 0.5 ) END CREATE( FISOLV ) RUN( FISOLV, BACK )
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291 Appendix H: GAMBIT/FIDAP Preprocessing Input for Chapter 9 H.1 Geometry and Meshing: GAMBIT Commands / GAMBIT Input File / GEOMETRY and MESHING / PROJECT: AirConditioned Hospital Operating Room / Threedimensional (3D) model, SI units / Constants: W x D x H of room, L: start height of upper zone / 20' x 7' x 10' = 6.10 x 2.15 x 3 m / $W = 6.10 $D = 2.15 $H = 3.00 $W0 = 6.00 $D0 = 2.10 $H0 = 2.90 / $W1 = 2.80 $W2 = 4.80 $D1 = 0.80 $D2 = 1.50 $H1 = 1.85 $H2 = 1.75 $H3 = 0.75 / $WL = 0.70 $DL = 0.55 $HL = 0.30 $Wb = 0.80 $Db = 0.60 $Hb = 0.40 / / Supply/Exhaust Grills: 24"x14" / $WW = 0.6096 $HH = 0.3556 $AA = 0.8 $BB = 0.6 $CC = 0.25 $XX = 0.15 / $Ws = $WW $Hs = $HH $As = $AA $Bs = $BB $Ys = 0.50 $Zs = 2.45 / $We = $WW $He = $HH
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Appendix H (Continued) 292$Ae = $AA $Be = $BB $Ye = 1.00 $Ze = 0.55 / / Mesh parameters (based on boundary layer thickness of 0.05 m) / $S = regular mesh size / $R = successive ratio (mesh edges) / $M = number of intervals (mesh edges) / $F = firstrow height (boundary layers) / $G = growth factor (boundary layers) / $N = number of rows (boundary layers) / $T = total depth (boundary layers) / $S = 0.1 / Total layer thickness = 0.05 m $R0 = 1.45 $M0 = 3 / Total layer thickness = 0.095 (Y) m or 0.122 m (Z) $Rs = 1.45 $Ms = 2 $Re = 1.45 $Me = 2 / Total layer thickness = 0.05 m $F = 0.011 $G = 1.45 $N = 3 / $Fs = 0.04 $Gs = 1.45 $Ns = 2 $Fe = 0.04 $Ge = 1.45 $Ne = 2 / / OPERATING ROOM (HALF): coor. sys. 1 (default) / volume create width $W depth $D height $H offset ($W/2) ($D/2) ($H/2) brick volume create width $W0 depth $D0 height $H0 offset ($W/2) ($D0/2) ($H/2) brick / / OCCUPIED ZONES: coor. sys. 2 / coordinate create cartesian oldsystem "c_sys.1" offset ($W/2) 0 0 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width $W2 depth $D height $H offset 0 ($D/2) ($H/2) brick volume create width $W2 depth $D2 height $H1 offset 0 ($D2/2) ($H1/2) brick volume create width $W1 depth $D1 height $H2 offset 0 ($D1/2) ($H2/2) brick
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Appendix H (Continued) 293volume create width $W1 depth $D1 height $H3 offset 0 ($D1/2) ($H3/2) brick / / SURGICAL LIGHTS: coor. sys. 3 / coordinate create cartesian oldsystem "c_sys.2" offset 0 0 ($H1+0.05) axis1 \ "x" angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width $WL depth $DL height $HL offset 0 ($DL/2) ($HL/2) brick volume create width $Wb depth $Db height $Hb offset 0 ($Db/2) ($HL/2) brick / / PATIENT (HALF): coor. sys. 4 / coordinate create cartesian oldsystem "c_sys.2" offset 0 0 ($H3+0.05) axis1 \ "x" angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width 1.7 depth 0.25 height 0.3 offset 0 0.125 0.15 brick volume create width 1.8 depth 0.3 height 0.4 offset 0 0.15 0.15 brick / / STAFF 1 (HALF): coor. sys. 5 / coordinate create cartesian oldsystem "c_sys.2" offset 1.35 0 0 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width 0.3 depth 0.25 height 1.7 offset 0.15 0.125 0.85 brick volume create width 0.4 depth 0.3 height 1.75 offset 0.15 0.15 0.875 brick / / STAFF 2 (HALF): coor. sys. 6 / coordinate create cartesian oldsystem "c_sys.2" offset 1.05 0 0 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width 0.3 depth 0.25 height 1.7 offset 0.15 0.125 0.85 brick volume create width 0.4 depth 0.3 height 1.75 offset 0.15 0.15 0.875 brick / / STAFF 3 (FULL): coor. sys. 7 / coordinate create cartesian oldsystem "c_sys.2" offset 0 0.45 0 axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width 0.5 depth 0.3 height 1.7 offset 0 0.15 0.85 brick volume create width 0.6 depth 0.4 height 1.75 offset 0 0.15 0.875 brick / / SUPPLY GRILL: coor. sys. 8 /
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Appendix H (Continued) 294coordinate create cartesian oldsystem "c_sys.1" offset 0 $Ys $Zs axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width $XX depth $Ws height $Hs offset ($XX/2) 0 0 brick volume create width $CC depth $As height $Bs offset ($CC/2) 0 0 brick / / EXHAUST GRILL: coor. sys. 9 / coordinate create cartesian oldsystem "c_sys.1" offset $W $Ye $Ze axis1 "x" \ angle1 0 axis2 "y" angle2 0 axis3 "z" angle3 0 rotation volume create width $XX depth $We height $He offset ($XX/2) 0 0 brick volume create width $CC depth $Ae height $Be offset ($CC/2) 0 0 brick / / ROOM WALLS BL CREATING AUXILIARY EDGES & VOLUMES / edge create straight "vertex.1" "vertex.9" edge create straight "vertex.2" "vertex.10" edge create straight "vertex.3" "vertex.11" edge create straight "vertex.4" "vertex.12" edge create straight "vertex.5" "vertex.13" edge create straight "vertex.6" "vertex.14" edge create straight "vertex.7" "vertex.15" edge create straight "vertex.8" "vertex.16" volume create wireframe "edge.1" "edge.2" "edge.3" "edge.4" "edge.13" \ "edge.14" "edge.16" "edge.15" "edge.241" "edge.242" "edge.243" "edge.244" volume create wireframe "edge.2" "edge.5" "edge.7" "edge.10" "edge.14" \ "edge.17" "edge.19" "edge.22" "edge.241" "edge.243" "edge.245" "edge.247" volume create wireframe "edge.3" "edge.6" "edge.8" "edge.11" "edge.15" \ "edge.18" "edge.20" "edge.23" "edge.242" "edge.244" "edge.246" "edge.248" volume create wireframe "edge.4" "edge.7" "edge.8" "edge.12" "edge.16" \ "edge.19" "edge.20" "edge.24" "edge.243" "edge.244" "edge.247" "edge.248" volume create wireframe "edge.9" "edge.10" "edge.11" "edge.12" "edge.21" \ "edge.22" "edge.23" "edge.24" "edge.245" "edge.246" "edge.247" "edge.248" volume delete "volume.1" lowertopology / / DIVIDING OPERATING ROOM INTO ZONES / volume split "volume.2" volumes "volume.3" connected bientity volume delete "volume.3" lowertopology volume split "volume.27" volumes "volume.4" connected bientity
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Appendix H (Continued) 295volume delete "volume.4" lowertopology volume split "volume.29" volumes "volume.5" connected bientity volume delete "volume.5" lowertopology volume subtract "volume.21" volumes "volume.12" "volume.14" "volume.16" \ keeptool volume subtract "volume.30" volumes "volume.10" "volume.12" "volume.14" \ "volume.16" volume subtract "volume.27" volumes "volume.8" / / LIGHTS BL CREATING AUXILIARY EDGES & VOLUMES / edge create straight "vertex.49" "vertex.241" edge create straight "vertex.50" "vertex.242" edge create straight "vertex.51" "vertex.243" edge create straight "vertex.52" "vertex.244" edge create straight "vertex.53" "vertex.245" edge create straight "vertex.54" "vertex.246" edge create straight "vertex.55" "vertex.63" edge create straight "vertex.56" "vertex.64" volume create wireframe "edge.73" "edge.74" "edge.75" "edge.76" "edge.389" \ "edge.391" "edge.392" "edge.393" "edge.397" "edge.398" "edge.399" "edge.400" volume create wireframe "edge.74" "edge.77" "edge.79" "edge.82" "edge.391" \ "edge.394" "edge.91" "edge.94" "edge.397" "edge.399" "edge.401" "edge.403" volume create wireframe "edge.75" "edge.78" "edge.80" "edge.83" "edge.392" \ "edge.395" "edge.92" "edge.95" "edge.398" "edge.400" "edge.402" "edge.404" volume create wireframe "edge.76" "edge.79" "edge.80" "edge.84" "edge.393" \ "edge.91" "edge.92" "edge.96" "edge.399" "edge.400" "edge.403" "edge.404" volume create wireframe "edge.81" "edge.82" "edge.83" "edge.84" "edge.396" \ "edge.94" "edge.95" "edge.96" "edge.401" "edge.402" "edge.403" "edge.404" / / PATIENT BL CREATING AUXILIARY EDGES & VOLUMES / edge create straight "vertex.65" "vertex.227" edge create straight "vertex.66" "vertex.228" edge create straight "vertex.67" "vertex.75" edge create straight "vertex.68" "vertex.76" edge create straight "vertex.69" "vertex.229" edge create straight "vertex.70" "vertex.230" edge create straight "vertex.71" "vertex.79" edge create straight "vertex.72" "vertex.80"
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Appendix H (Continued) 296volume create wireframe "edge.97" "edge.98" "edge.99" "edge.100" "edge.366" \ "edge.110" "edge.111" "edge.112" "edge.405" "edge.406" "edge.407" \ "edge.408" volume create wireframe "edge.98" "edge.101" "edge.103" "edge.106" "edge.110" \ "edge.367" "edge.115" "edge.118" "edge.405" "edge.407" "edge.409" \ "edge.411" volume create wireframe "edge.99" "edge.102" "edge.104" "edge.107" "edge.111" \ "edge.368" "edge.116" "edge.119" "edge.406" "edge.408" "edge.410" \ "edge.412" volume create wireframe "edge.100" "edge.103" "edge.104" "edge.108" \ "edge.112" "edge.115" "edge.116" "edge.120" "edge.407" "edge.408" \ "edge.411" "edge.412" volume create wireframe "edge.105" "edge.106" "edge.107" "edge.108" \ "edge.369" "edge.118" "edge.119" "edge.120" "edge.409" "edge.410" \ "edge.411" "edge.412" / / STAFF 1 BL CREATING AUXILIARY EDGES & VOLUMES / edge create straight "vertex.81" "vertex.205" edge create straight "vertex.82" "vertex.206" edge create straight "vertex.83" "vertex.207" edge create straight "vertex.84" "vertex.208" edge create straight "vertex.85" "vertex.179" edge create straight "vertex.86" "vertex.231" edge create straight "vertex.87" "vertex.232" edge create straight "vertex.88" "vertex.233" volume create wireframe "edge.122" "edge.125" "edge.127" "edge.130" \ "edge.330" "edge.333" "edge.335" "edge.287" "edge.290" "edge.371" \ "edge.373" "edge.413" "edge.415" "edge.417" "edge.419" volume create wireframe "edge.123" "edge.126" "edge.128" "edge.131" \ "edge.331" "edge.334" "edge.336" "edge.338" "edge.370" "edge.140" \ "edge.374" "edge.414" "edge.416" "edge.418" "edge.420" volume create wireframe "edge.124" "edge.127" "edge.128" "edge.132" \ "edge.332" "edge.335" "edge.336" "edge.339" "edge.371" "edge.140" \ "edge.375" "edge.415" "edge.416" "edge.419" "edge.420" volume create wireframe "edge.129" "edge.130" "edge.131" "edge.132" \ "edge.292" "edge.373" "edge.374" "edge.375" "edge.417" "edge.418" \ "edge.419" "edge.420" / / STAFF 2 BL CREATING AUXILIARY EDGES & VOLUMES / edge create straight "vertex.97" "vertex.212" edge create straight "vertex.98" "vertex.213" edge create straight "vertex.99" "vertex.214" edge create straight "vertex.100" "vertex.215" edge create straight "vertex.101" "vertex.234" edge create straight "vertex.102" "vertex.180" edge create straight "vertex.103" "vertex.235" edge create straight "vertex.104" "vertex.236" volume create wireframe "edge.146" "edge.149" "edge.151" "edge.154" \
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Appendix H (Continued) 297 "edge.342" "edge.345" "edge.347" "edge.350" "edge.376" "edge.163" \ "edge.379" "edge.421" "edge.423" "edge.425" "edge.427" volume create wireframe "edge.147" "edge.150" "edge.152" "edge.155" \ "edge.343" "edge.346" "edge.348" "edge.351" "edge.291" "edge.377" "edge.59" \ "edge.422" "edge.424" "edge.426" "edge.428" volume create wireframe "edge.148" "edge.151" "edge.152" "edge.156" \ "edge.344" "edge.347" "edge.348" "edge.352" "edge.163" "edge.377" \ "edge.380" "edge.423" "edge.424" "edge.427" "edge.428" volume create wireframe "edge.153" "edge.154" "edge.155" "edge.156" \ "edge.378" "edge.379" "edge.59" "edge.380" "edge.425" "edge.426" "edge.427" \ "edge.428" / / STAFF 3 BL CREATING AUXILIARY EDGES & VOLUMES / edge create straight "vertex.113" "vertex.219" edge create straight "vertex.114" "vertex.220" edge create straight "vertex.115" "vertex.221" edge create straight "vertex.116" "vertex.222" edge create straight "vertex.117" "vertex.237" edge create straight "vertex.118" "vertex.238" edge create straight "vertex.119" "vertex.239" edge create straight "vertex.120" "vertex.240" volume create wireframe "edge.169" "edge.173" "edge.174" "edge.177" \ "edge.353" "edge.357" "edge.358" "edge.361" "edge.185" "edge.186" \ "edge.384" "edge.429" "edge.430" "edge.433" "edge.434" volume create wireframe "edge.170" "edge.173" "edge.175" "edge.178" \ "edge.354" "edge.357" "edge.359" "edge.362" "edge.185" "edge.382" \ "edge.385" "edge.429" "edge.431" "edge.433" "edge.435" volume create wireframe "edge.171" "edge.174" "edge.176" "edge.179" \ "edge.355" "edge.358" "edge.360" "edge.363" "edge.186" "edge.383" \ "edge.386" "edge.430" "edge.432" "edge.434" "edge.436" volume create wireframe "edge.172" "edge.175" "edge.176" "edge.180" \ "edge.356" "edge.359" "edge.360" "edge.364" "edge.382" "edge.383" \ "edge.388" "edge.431" "edge.432" "edge.435" "edge.436" volume create wireframe "edge.177" "edge.178" "edge.179" "edge.180" \ "edge.384" "edge.385" "edge.386" "edge.388" "edge.433" "edge.434" \ "edge.435" "edge.436" / / ZONE 1 & UNDER TABLE / volume split "volume.30" volumes "volume.6" connected bientity volume delete "volume.6" lowertopology / / SUPPLY GRILL CREATING AUXILIARY EDGES & VOLUMES / volume subtract "volume.22" volumes "volume.18" keeptool volume subtract "volume.28" volumes "volume.18" / edge create straight "vertex.129" "vertex.267" edge create straight "vertex.131" "vertex.269" edge create straight "vertex.133" "vertex.271"
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Appendix H (Continued) 298edge create straight "vertex.135" "vertex.273" edge create straight "vertex.130" "vertex.138" edge create straight "vertex.132" "vertex.140" edge create straight "vertex.134" "vertex.142" edge create straight "vertex.136" "vertex.144" volume create wireframe "edge.194" "edge.193" "edge.196" "edge.195" \ "edge.480" "edge.479" "edge.474" "edge.481" "edge.205" "edge.489" \ "edge.207" "edge.491" "edge.492" "edge.495" "edge.496" volume create wireframe "edge.197" "edge.193" "edge.201" "edge.198" \ "edge.482" "edge.479" "edge.470" "edge.483" "edge.205" "edge.490" \ "edge.210" "edge.491" "edge.493" "edge.495" "edge.497" volume create wireframe "edge.199" "edge.196" "edge.204" "edge.200" \ "edge.484" "edge.474" "edge.488" "edge.485" "edge.489" "edge.216" \ "edge.212" "edge.492" "edge.494" "edge.496" "edge.498" volume create wireframe "edge.202" "edge.201" "edge.204" "edge.203" \ "edge.486" "edge.470" "edge.488" "edge.487" "edge.490" "edge.216" \ "edge.215" "edge.493" "edge.494" "edge.497" "edge.498" volume create wireframe "edge.195" "edge.198" "edge.200" "edge.203" \ "edge.207" "edge.210" "edge.212" "edge.215" "edge.495" "edge.496" \ "edge.497" "edge.498" / / EXAUST GRILL CREATING AUXILIARY EDGES & VOLUMES / volume subtract "volume.23" volumes "volume.20" keeptool volume subtract "volume.2" volumes "volume.20" / edge create straight "vertex.146" "vertex.284" edge create straight "vertex.148" "vertex.286" edge create straight "vertex.150" "vertex.288" edge create straight "vertex.152" "vertex.290" edge create straight "vertex.145" "vertex.153" edge create straight "vertex.147" "vertex.155" edge create straight "vertex.149" "vertex.157" edge create straight "vertex.151" "vertex.159" volume create wireframe "edge.219" "edge.217" "edge.220" "edge.218" \ "edge.512" "edge.504" "edge.513" "edge.511" "edge.521" "edge.232" \ "edge.230" "edge.523" "edge.524" "edge.527" "edge.528" volume create wireframe "edge.222" "edge.217" "edge.225" "edge.221" \ "edge.515" "edge.504" "edge.518" "edge.514" "edge.521" "edge.237" \ "edge.233" "edge.523" "edge.525" "edge.527" "edge.529" volume create wireframe "edge.224" "edge.220" "edge.228" "edge.223" \ "edge.517" "edge.513" "edge.500" "edge.516" "edge.232" "edge.522" \ "edge.235" "edge.524" "edge.526" "edge.528" "edge.530" volume create wireframe "edge.227" "edge.225" "edge.228" "edge.226" \ "edge.520" "edge.518" "edge.500" "edge.519" "edge.237" "edge.522" \ "edge.238" "edge.525" "edge.526" "edge.529" "edge.530" volume create wireframe "edge.218" "edge.221" "edge.223" "edge.226" \ "edge.230" "edge.233" "edge.235" "edge.238" "edge.527" "edge.528" \ "edge.529" "edge.530" / / MESHING: CREATING 3D HEXAHEDRAL ELEMENT MESH / / OCCUPIED ZONE, LIGHTS & OCCUPANTS
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Appendix H (Continued) 299/ edge mesh "edge.241" "edge.242" "edge.243" "edge.244" "edge.245" "edge.246" \ "edge.247" "edge.248" "edge.397" "edge.398" "edge.399" "edge.400" \ "edge.401" "edge.402" "edge.403" "edge.404" "edge.405" "edge.406" \ "edge.407" "edge.408" "edge.409" "edge.410" "edge.411" "edge.412" \ "edge.413" "edge.414" "edge.415" "edge.416" "edge.417" "edge.418" \ "edge.419" "edge.420" "edge.421" "edge.422" "edge.423" "edge.424" \ "edge.425" "edge.426" "edge.427" "edge.428" "edge.429" "edge.430" \ "edge.431" "edge.432" "edge.433" "edge.434" "edge.435" "edge.436" \ successive ratio1 $R0 intervals $M0 / blayer create first $F growth $G rows $N transition 1 trows 0 blayer attach "b_layer.1" face "face.63" "face.64" "face.65" "face.75" \ "face.76" "face.77" "face.86" "face.87" "face.88" "face.89" edge "edge.122" \ "edge.123" "edge.124" "edge.146" "edge.147" "edge.148" "edge.169" \ "edge.170" "edge.171" "edge.172" / blayer create first $F growth $G rows ($N1) transition 1 trows 0 blayer attach "b_layer.2" face "face.230" "face.234" "face.231" "face.235" \ "face.241" "face.245" "face.242" "face.246" "face.252" "face.253" \ "face.256" "face.259" edge "edge.413" "edge.414" "edge.415" "edge.416" \ "edge.421" "edge.422" "edge.423" "edge.424" "edge.429" "edge.430" \ "edge.431" "edge.432" / volume mesh "volume.54" "volume.30" "volume.29" "volume.27" submap size $S volume mesh "volume.31" "volume.32" "volume.33" "volume.34" "volume.35" map volume mesh "volume.36" "volume.37" "volume.38" "volume.39" "volume.40" map volume mesh "volume.41" "volume.42" "volume.43" "volume.44" map volume mesh "volume.45" "volume.46" "volume.47" "volume.48" map volume mesh "volume.49" "volume.50" "volume.51" "volume.52" "volume.53" map / / SUPPLY SIDE / edge mesh "edge.492" "edge.491" "edge.494" "edge.493" successive ratio1 $Rs \ intervals $Ms / blayer create first $F growth $G rows $N transition 1 trows 0 blayer attach "b_layer.3" face "face.97" "face.101" "face.98" "face.102" edge \ "edge.194" "edge.199" "edge.197" "edge.202" / blayer create first $F growth $G rows ($N1) transition 1 trows 0
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Appendix H (Continued) 300blayer attach "b_layer.4" face "face.292" "face.291" "face.298" "face.295" \ edge "edge.492" "edge.491" "edge.494" "edge.493" / blayer create first $Fs growth $Gs rows $Ns transition 1 trows 0 blayer attach "b_layer.5" face "face.99" "face.99" "face.99" "face.99" edge \ "edge.199" "edge.197" "edge.194" "edge.202" / volume mesh "volume.28" submap size $S volume mesh "volume.55" "volume.57" "volume.56" "volume.58" map volume mesh "volume.59" "volume.17" map volume mesh "volume.22" cooper source "face.9" "face.3" / / EXHAUST SIDE / edge mesh "edge.523" "edge.524" "edge.525" "edge.526" successive ratio1 $Re \ intervals $Me / blayer create first $F growth $G rows $N transition 1 trows 0 blayer attach "b_layer.6" face "face.109" "face.110" "face.113" "face.114" \ edge "edge.219" "edge.222" "edge.224" "edge.227" / blayer create first $F growth $G rows ($N1) transition 1 trows 0 blayer attach "b_layer.7" face "face.313" "face.314" "face.317" "face.320" \ edge "edge.523" "edge.524" "edge.525" "edge.526" / blayer create first $Fe growth $Ge rows $Ne transition 1 trows 0 blayer attach "b_layer.8" face "face.112" "face.112" "face.112" "face.112" \ edge "edge.219" "edge.227" "edge.222" "edge.224" / volume mesh "volume.2" submap size $S volume mesh "volume.60" "volume.61" "volume.62" "volume.63" map volume mesh "volume.64" "volume.19" map volume mesh "volume.23" cooper source "face.10" "face.4" / / SIDE WALL, CEILING, & FLOOR / volume mesh "volume.24" "volume.25" map volume mesh "volume.21" cooper source "face.180" "face.154" "face.146" \ "face.134" "face.7" "face.181" / volume delete "volume.7" "volume.9" "volume.11" "volume.13" "volume.15" \ lowertopology / / PHYSICAL SETTINGS /
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Appendix H (Continued) 301solver select "FIDAP" / physics create "air" ctype "FLUID" volume \ "volume.37" "volume.38" "volume.39" "volume.40" \ "volume.41" "volume.42" "volume.43" "volume.44" \ "volume.45" "volume.46" "volume.47" "volume.48" \ "volume.49" "volume.50" "volume.51" "volume.52" "volume.53" \ "volume.30" "volume.29" "volume.54" "volume.36" \ "volume.2" "volume.7" "volume.9" \ "volume.11" "volume.13" "volume.15" "volume.17" "volume.19" "volume.21" \ "volume.22" "volume.23" "volume.24" "volume.25" "volume.54" "volume.28" \ "volume.27" "volume.29" "volume.31" "volume.32" "volume.33" "volume.34" \ "volume.35" "volume.36" "volume.37" "volume.38" "volume.39" "volume.40" \ "volume.41" "volume.42" "volume.43" "volume.44" "volume.45" "volume.46" \ "volume.47" "volume.48" "volume.49" "volume.50" "volume.51" "volume.52" \ "volume.53" "volume.30" "volume.55" "volume.56" "volume.57" "volume.58" \ "volume.59" "volume.60" "volume.61" "volume.62" "volume.63" "volume.64" / physics create "supply" btype "PLOT" face "face.99" physics create "exhaust" btype "PLOT" face "face.112" physics create "symmetry" btype "PLOT" face "face.204" "face.147" "face.189" \ "face.269" "face.8" "face.137" "face.132" "face.182" "face.178" "face.121" \ "face.205" "face.209" "face.212" "face.216" "face.217" "face.221" \ "face.224" "face.228" "face.230" "face.234" "face.239" "face.241" \ "face.245" "face.250" "face.125" "face.128" physics create "ceiling" btype "WALL" face "face.6" physics create "floor" btype "WALL" face "face.181" "face.229" "face.233" \ "face.237" "face.240" "face.244" "face.248" "face.251" "face.255" \ "face.258" "face.261" physics create "wall_side" btype "WALL" face "face.5" physics create "wall_left" btype "WALL" face "face.3" "face.290" "face.297" \ "face.294" "face.300" physics create "wall_right" btype "WALL" face "face.4" "face.312" "face.316" \ "face.319" "face.322" physics create "light_face" btype "WALL" face "face.37" physics create "light_back" btype "WALL" face "face.39" "face.40" "face.41" \ "face.42" physics create "table" btype "WALL" face "face.49"
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Appendix H (Continued) 302physics create "patient" btype "WALL" face "face.51" "face.52" "face.53" \ "face.54" physics create "staff_1" btype "WALL" face "face.63" "face.64" "face.65" \ "face.66" physics create "staff_2" btype "WALL" face "face.75" "face.76" "face.77" \ "face.78" physics create "staff_3" btype "WALL" face "face.86" "face.87" "face.88" \ "face.89" "face.90" / / EXPORTING MESH / $ID = GETIDENT() $NEUTRALFILE = $ID + ".FDNEUT" export fidap $NEUTRALFILE H.2 Simulation Settings: FIDAP Commands / FIDAP Input File / SIMULATION SETTINGS / PROJECT: AirConditioned Hospital Operating Room / Threedimensional (3D) model, SI units / Neutral file name for database of model geometry & mesh / $NEUTRALFILE = "mesh.FDNEUT" / / CONVERSION OF NEUTRAL FILE TO FIDAP Database / FICONV( NEUTRAL ) INPUT( FILE = $NEUTRALFILE ) OUTPUT( DELETE ) END / TITLE Hospital Operating Room, 3D model / / CONSTANTS / $V_SUPPLY = 1. $UX_0 = $V_SUPPLY $UY_0 = 0. $UZ_0 = 0. / $T_SUPPLY = 20. $F_LFACE = 100. $F_LBACK = 5.
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Appendix H (Continued) 303$T_PATIENT = 34. $T_STAFF = 34. / $W_SUPPLY = 0.01 $FW_PATIENT = 2.5E6 $FW_STAFF = 4.0E6 / $C_SUPPLY = 0. $FC_PATIENT = 1.0E5 / IF ( $T_SUPPLY .EQ. 0 ) $T_MIN = 1.E20 ELSE $T_MIN = $T_SUPPLY ENDIF / IF ( $W_SUPPLY .EQ. 0 ) $W_MIN = 1.E20 ELSE $W_MIN = $W_SUPPLY ENDIF / IF ( $C_SUPPLY .EQ. 0 ) $C_MIN = 1.E20 ELSE $C_MIN = $C_SUPPLY ENDIF / $G = 9.8 $RHO = 1.2 $MU = 1.8E5 $K = 0.026 $CP = 1004. $BETA = 0.0034 $TREF = 20. $D_1 = 2.5e05 $D_2 = 1.2e05 / FIPREP / / PROBLEM SETUP / PROBLEM( 3D, TURBULENT, NONLINEAR, BUOYANCY, SPECIES = 1, SPECIES = 2 ) GRAVITY( MAGNITUDE = $G ) EXECUTION( NEWJOB ) PRINTOUT( NONE ) DATAPRINT( NONE ) / / CONTINUUM ENTITIES / ENTITY( NAME = "air", FLUID, SPEC=1, MDIF="H2O", SPEC=2, MDIF="ALC" ) /
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Appendix H (Continued) 304/ BOUNDARY ENTITIES / ENTITY( NAME = "supply", PLOT ) ENTITY( NAME = "exhaust", PLOT ) ENTITY( NAME = "symmetry", PLOT ) ENTITY( NAME = "wall_side", WALL ) ENTITY( NAME = "wall_left", WALL ) ENTITY( NAME = "wall_right", WALL ) ENTITY( NAME = "floor", WALL ) ENTITY( NAME = "ceiling", WALL ) ENTITY( NAME = "table", WALL ) ENTITY( NAME = "light_face", WALL ) ENTITY( NAME = "light_back", WALL ) ENTITY( NAME = "patient", WALL ) ENTITY( NAME = "staff_1", WALL ) ENTITY( NAME = "staff_2", WALL ) ENTITY( NAME = "staff_3", WALL ) / / SOLUTION PARAMETERS / SOLUTION( SEGREGATED = 400, CR, CGS, VELCONV = .01, NCGC = 1.E6, SCGC = 1.E6, SCHANGE = .0 ) PRESSURE( MIXED = 1.E8, DISCONTINUOUS ) RELAX( HYBRID ) OPTIONS( UPWINDING ) CLIPPING( MINIMUM ) 0 0 0 0 $T_MIN 0 0 0 $W_MIN $C_MIN CLIPPING( MAXIMUM ) 0 0 0 0 0 0 0 0 1. 1. / / MATERIAL PROPERTIES / / Partial list of Material Properties data / DENSITY( CONSTANT = $RHO ) VISCOSITY( CONSTANT = $MU, MIXLENGTH ) CONDUCTIVITY( CONSTANT = $K ) SPECIFICHEAT( CONSTANT = $CP ) VOLUMEXPANSION( CONSTANT = $BETA, REFTEMP = $TREF ) DIFFUSIVITY( SET = "H2O", CONS = $D_1 ) DIFFUSIVITY( SET = "ALC", CONS = $D_2 ) / / BOUNDARY CONDITIONS / BCNODE( VELO, CONSTANT, ENTITY = "supply", X = $UX_0, Y = $UY_0, Z = $UZ_0 ) BCNODE( UY, ZERO, ENTITY = "symmetry" ) BCNODE( VELO, ZERO, ENTITY = "ceiling" ) BCNODE( VELO, ZERO, ENTITY = "wall_side" ) BCNODE( VELO, ZERO, ENTITY = "wall_left" )
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Appendix H (Continued) 305BCNODE( VELO, ZERO, ENTITY = "wall_right" ) BCNODE( VELO, ZERO, ENTITY = "floor" ) BCNODE( VELO, ZERO, ENTITY = "light_face" ) BCNODE( VELO, ZERO, ENTITY = "light_back" ) BCNODE( VELO, ZERO, ENTITY = "table" ) BCNODE( VELO, ZERO, ENTITY = "patient" ) BCNODE( VELO, ZERO, ENTITY = "staff_1" ) BCNODE( VELO, ZERO, ENTITY = "staff_2" ) BCNODE( VELO, ZERO, ENTITY = "staff_3" ) / BCNODE( TEMP, CONSTANT = $T_SUPPLY, ENTITY = "supply" ) BCFLUX( HEAT, CONSTANT = $F_LFACE, ENTITY = "light_face" ) BCFLUX( HEAT, CONSTANT = $F_LBACK, ENTITY = "light_back" ) BCNODE( TEMP, CONSTANT = $T_PATIENT, ENTITY = "patient" ) BCNODE( TEMP, CONSTANT = $T_STAFF, ENTITY = "staff_1" ) BCNODE( TEMP, CONSTANT = $T_STAFF, ENTITY = "staff_2" ) BCNODE( TEMP, CONSTANT = $T_STAFF, ENTITY = "staff_3" ) / BCNODE( SPEC = 1, CONSTANT = $W_SUPPLY, ENTITY = "supply" ) BCFLUX( SPEC = 1, CONSTANT = $FW_PATIENT, ENTITY = "patient" ) BCFLUX( SPEC = 1, CONSTANT = $FW_STAFF, ENTITY = "staff_1" ) BCFLUX( SPEC = 1, CONSTANT = $FW_STAFF, ENTITY = "staff_2" ) BCFLUX( SPEC = 1, CONSTANT = $FW_STAFF, ENTITY = "staff_3" ) / BCNODE( SPEC = 2, CONSTANT = $C_SUPPLY, ENTITY = "supply" ) BCFLUX( SPEC = 2, CONSTANT = $FC_PATIENT, ENTITY = "patient" ) / END / CREATE( FISOLV ) RUN( FISOLV, BACKGROUND )
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306 Appendix I: MATLAB Programs for 3D Solution Visualization I.1 Import Numerical Solution from FIDAP function ReadFidapSolution3D global X % X coordinate global Y % Y coordinate global Z % Z coordinate global UX % X component velocity global UY % Y component velocity global UZ % Z component velocity global SP % Speed global P % Pressure global T % Temperature global RH % FIDAP userdefined variable (relative humidity) global S2 % Species 2 (contaminant gas) % '*.FPNEUT': solution neutral files exported from FIDAP/FIPOST % Speed (SP) can be read from a FIDAP neutral files if available or % calculated from velocity components as SP = sqrt(UX.^2+UY.^2+UZ.^2) % Replace proper directory path and file names in next 2 lines folder_name = '...\OR_HVAC\NEUTRAL'; file_names = {'UX.FPNEUT','UY.FPNEUT','UZ.FPNEUT','P.FPNEUT',... 'T.FPNEUT','SP.FPNEUT','RH.FPNEUT','S2.FPNEUT'}; num_file = length(file_names); for k=1:num_file file_name=char(file_names(k)); full_path = strcat(folder_name,'\',file_name); [Vname,N,F,X,Y,Z] = FD2ML3D(full_path); {file_name;Vname;N} switch Vname case 'X COMP. VELOC. UX = F; case 'Y COMP. VELOC. UY = F; case 'Z COMP. VELOC. UZ = F; case 'SPEED SP = F; case 'PRESSURE P = F; case 'TEMPERATURE T = F; case 'USER FUNCTION RH = F; case 'SPECIES 2 S2 = F; end end
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Appendix I (Continued) 307function [Vname,N,F,X,Y,Z] = FD2ML3D(fpneut_name) [Vname,N] = textread(fpneut_name,'%20c %d',1); A = zeros(4,N); fid = fopen(fpneut_name); fgets(fid); A = fscanf(fid,'%*d %f %f %f %f',[4 N]); fclose(fid); F = A(1,:); X = A(2,:); Y = A(3,:); Z = A(4,:); I.2 Solution Visualization for 3D Operating Room (Chapter 9) function OR_Plot3D_Prep % Prepare data for 3D plots global X global Y global Z global UX global UY global UZ global SP global P global T global S2 global RH global XI global YI global ZI global UI global VI global WI global SI global PI global TI global CI global RI global xmin global xmax global ymin global ymax global zmin global zmax d = 0.025; eps = 0.001;
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Appendix I (Continued) 308xmin = min(X); xmax = max(X); ymin = min(Y); ymax = max(Y); zmin = min(Z); zmax = max(Z); rx = [xmin:d:xmax]; if rx(end)
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Appendix I (Continued) 309for i=1:3 for j=1:3 hlines = streamline(XI,YI,ZI,UI,VI,WI,sx(i,1,j),sy(i,1,j),sz(i,1,j)); set(hlines,'LineWidth',2,'Color',cmap(i+3*(j1),:)) end end legend({'1','2','3','4','5','6','7','8','9'},... 'Position',[0.5 0.004 0 0.066],... 'Orientation','horizontal'); hold on plot3(sx(:),sy(:),sz(:),'*k','MarkerSize',5,'LineWidth',1); hold off Draw_OperatingRoom_3D_2 view(30,15) camva(6.8) function OR_Plot3D_Pressure global XI global YI global ZI global PI isovalue = 0.9:0.05:1.2; figure(3) clf reset for i=1:length(isovalue) isosurface(XI,YI,ZI,PI,isovalue(i)) end Draw_OperatingRoom_3D_2 set(gca,'CLim',[0.9 1.25]) colorbar('SouthOutside') view(30,15) function OR_Plot3D_ContaminantConcentration global XI global YI global ZI global CI figure(4) clf reset slice(XI,YI,ZI,1e6*CI,[1.85 3.05 4.25],[1.5],[0.55 2.45]) shading interp; Draw_OperatingRoom_3D_2 set(gca,'CLim',[0 180]) colorbar('SouthOutside') view(30,15)
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Appendix I (Continued) 310function OR_Plot3D_Temperature global XI global YI global ZI global TI figure(5) clf reset slice(XI,YI,ZI,TI,[1.85 3.05 4.25],[1.5],[0.55 2.45]) shading interp; Draw_OperatingRoom_3D_2 set(gca,'CLim',[20 27]) colorbar('SouthOutside') view(30,15) function OR_Plot3D_RelativeHumidity global XI global YI global ZI global RI figure(6) clf reset slice(XI,YI,ZI,100*RI,[1.85 3.05 4.25],[1.5],[0.55 2.45]) shading interp; Draw_OperatingRoom_3D_2 set(gca,'CLim',[50 66]) colorbar('SouthOutside') view(30,15) function Draw_OperatingRoom_3D(status) global xmin global xmax global ymin global ymax global zmin global zmax xmin = 0; xmax = 6.1; ymin = 0; ymax = 2.15; zmin = 0 zmax = 3.0; gr = [0.4 0.4 0.4]; color1 = 'k'; ys = 1.0; zs = 2.45; ws = 0.6096;
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Appendix I (Continued) 311hs = 0.3556; ye = 1.0; ze = 0.55; we = 0.6096; he = 0.3556; daspect([1,1,1]) axis([ xmin xmax ymin ymax zmin zmax ]) box on grid off xx = [xmin xmin xmin xmin xmin]; yy = [ysws/2 ysws/2 ys+ws/2 ys+ws/2 ysws/2]; zz = [zshs/2 zs+hs/2 zs+hs/2 zshs/2 zshs/2]; line(xx,yy,zz,'Color',color1) xx = [xmax xmax xmax xmax xmax]; yy = [yewe/2 yewe/2 ye+we/2 ye+we/2 yewe/2]; zz = [zehe/2 ze+he/2 ze+he/2 zehe/2 zehe/2]; line(xx,yy,zz,'Color',color1) % if ((nargin==0)((nargin>0)&(status>0))) color_f = 'k'; color_e = 'w'; faces_matrix = [ 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8; 1 2 3 4; 5 6 7 8 ]; % surgical light x1 = 2.7; x2 = x1 + 0.7; y1 = 0; y2 = y1 + 0.65; z1 = 1.9; z2 = z1 + 0.3; vertex_matrix = [ x1 y1 z1; x2 y1 z1; x2 y2 z1; x1 y2 z1; x1 y1 z2; x2 y1 z2; x2 y2 z2; x1 y2 z2 ]; patch('Vertices',vertex_matrix,'Faces',faces_matrix,'FaceColor',color _f,'EdgeColor',color_e) % patient x1 = 2.2; x2 = x1 + 1.7; y1 = 0; y2 = y1 + 0.25; z1 = 0.8; z2 = z1 + 0.3; vertex_matrix = [ x1 y1 z1; x2 y1 z1; x2 y2 z1; x1 y2 z1; x1 y1 z2; x2 y1 z2; x2 y2 z2; x1 y2 z2 ]; patch('Vertices',vertex_matrix,'Faces',faces_matrix,'FaceColor',color _f,'EdgeColor',color_e) % staff 1 x1 = 1.7; x2 = x1 + 0.3;
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Appendix I (Continued) 312 y1 = 0; y2 = y1 + 0.25; z1 = 0; z2 = z1 + 1.7; vertex_matrix = [ x1 y1 z1; x2 y1 z1; x2 y2 z1; x1 y2 z1; x1 y1 z2; x2 y1 z2; x2 y2 z2; x1 y2 z2 ]; patch('Vertices',vertex_matrix,'Faces',faces_matrix,'FaceColor',color _f,'EdgeColor',color_e) % staff 2 x1 = 4.1; x2 = x1 + 0.3; y1 = 0; y2 = y1 + 0.25; z1 = 0; z2 = z1 + 1.7; vertex_matrix = [ x1 y1 z1; x2 y1 z1; x2 y2 z1; x1 y2 z1; x1 y1 z2; x2 y1 z2; x2 y2 z2; x1 y2 z2 ]; patch('Vertices',vertex_matrix,'Faces',faces_matrix,'FaceColor',color _f,'EdgeColor',color_e) % staff 3 x1 = 2.8; x2 = x1 + 0.5; y1 = 0.45; y2 = y1 + 0.3; z1 = 0; z2 = z1 + 1.7; vertex_matrix = [ x1 y1 z1; x2 y1 z1; x2 y2 z1; x1 y2 z1; x1 y1 z2; x2 y1 z2; x2 y2 z2; x1 y2 z2 ]; patch('Vertices',vertex_matrix,'Faces',faces_matrix,'FaceColor',color _f,'EdgeColor',color_e) end
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About the Author Son Hong Ho was born in Saigon, Viet nam, on March 4, 1971. He received a Degree of Engineer in Mech anical Engineering with honor s from the University of Technology, Ho Chi Minh city (Saigon), Viet nam, in 1995 followed by working there as a Research Engineer for 6 year s. He immigrated to the Unit ed States in 2001 and became a naturalized citizen in 2007. He entered the Ma ster's program at the University of South Florida (USF) in 2002 and receiv ed his Master of Science in Mechanical Engineering (MSME) degree in 2004. He has been continui ng his Ph.D. program at USF since then. While studying in the M.S. and Ph.D. progr ams at USF, Mr. Ho has been working as a Research Assistant on se veral projects funded by NASA, NIH, and NSF. He has coauthored more than ten technical research ar ticles. He has also been working for Meckler Forensic Group on several projects as a Research Engineer.
